Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2015, Volume 167, Issue 2, pp. 409 - 429

... of results proved recently in this direction. For this purpose, we analyze the asymptotic behavior of compositions of finitely many firmly nonexpansive mappings focusing...

p$$ p -Uniformly convex geodesic space | 53C23 | Mathematics | Theory of Computation | Optimization | CAT $$(\kappa )$$ ( κ ) space | Convex feasibility problem | Calculus of Variations and Optimal Control; Optimization | Convex optimization | Firmly nonexpansive mapping | 47H09 | 49M27 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | CAT(κ) space | p-Uniformly convex geodesic space | MATHEMATICS, APPLIED | INEQUALITIES | METRIC-SPACES | GEODESIC SPACES | UNIFORM CONVEXITY | CAT(kappa) space | PROXIMAL POINT ALGORITHM | VECTOR-FIELDS | NONLINEAR OPERATORS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BANACH-SPACES | HADAMARD SPACES | CONVERGENCE | Minimization | Mapping | Asymptotic properties | Regularity | Convergence

p$$ p -Uniformly convex geodesic space | 53C23 | Mathematics | Theory of Computation | Optimization | CAT $$(\kappa )$$ ( κ ) space | Convex feasibility problem | Calculus of Variations and Optimal Control; Optimization | Convex optimization | Firmly nonexpansive mapping | 47H09 | 49M27 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | CAT(κ) space | p-Uniformly convex geodesic space | MATHEMATICS, APPLIED | INEQUALITIES | METRIC-SPACES | GEODESIC SPACES | UNIFORM CONVEXITY | CAT(kappa) space | PROXIMAL POINT ALGORITHM | VECTOR-FIELDS | NONLINEAR OPERATORS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BANACH-SPACES | HADAMARD SPACES | CONVERGENCE | Minimization | Mapping | Asymptotic properties | Regularity | Convergence

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2013, Volume 2013, Issue 1, pp. 1 - 43

In this paper, we introduce a new class of mappings called Bregman weak relatively nonexpansive mappings and propose new hybrid iterative algorithms for finding common fixed points of an infinite...

uniformly smooth function | Mathematical and Computational Biology | uniformly convex function | Mathematics | Topology | strong convergence | Bregman function | fixed point | Analysis | Mathematics, general | Applications of Mathematics | Differential Geometry | Bregman weak relatively nonexpansive mapping | Strong convergence | Uniformly smooth function | Uniformly convex function | Fixed point | EXISTENCE | ALGORITHM | STRONG-CONVERGENCE THEOREMS | NONLINEAR INTEGRAL-EQUATIONS | MATHEMATICS | COMMON FIXED-POINT | EQUILIBRIUM PROBLEMS | MONOTONE-OPERATORS | Fixed point theory | Usage | Banach spaces | Contraction operators

uniformly smooth function | Mathematical and Computational Biology | uniformly convex function | Mathematics | Topology | strong convergence | Bregman function | fixed point | Analysis | Mathematics, general | Applications of Mathematics | Differential Geometry | Bregman weak relatively nonexpansive mapping | Strong convergence | Uniformly smooth function | Uniformly convex function | Fixed point | EXISTENCE | ALGORITHM | STRONG-CONVERGENCE THEOREMS | NONLINEAR INTEGRAL-EQUATIONS | MATHEMATICS | COMMON FIXED-POINT | EQUILIBRIUM PROBLEMS | MONOTONE-OPERATORS | Fixed point theory | Usage | Banach spaces | Contraction operators

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1812, 12/2014, Volume 2014, Issue 1, pp. 1 - 17

The purpose of this paper is to construct a new iterative scheme and to get a strong convergence theorem for a countable family of relatively quasi-nonexpansive mappings and a system of equilibrium...

equilibrium problems | generalized f -projection operator | hybrid algorithm | Mathematical and Computational Biology | Analysis | relatively quasi-nonexpansive mapping | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | uniformly closed mappings | MATHEMATICS | generalized f-projection operator | INEQUALITIES | BANACH-SPACES | WEAK-CONVERGENCE | OPERATORS | Fixed point theory | Usage | Convergence (Mathematics) | Banach spaces | Contraction operators

equilibrium problems | generalized f -projection operator | hybrid algorithm | Mathematical and Computational Biology | Analysis | relatively quasi-nonexpansive mapping | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | uniformly closed mappings | MATHEMATICS | generalized f-projection operator | INEQUALITIES | BANACH-SPACES | WEAK-CONVERGENCE | OPERATORS | Fixed point theory | Usage | Convergence (Mathematics) | Banach spaces | Contraction operators

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2011, Volume 2011, Issue 1, pp. 1 - 24

...-asymptotically nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, and the set of solutions of a system of generalized mixed equilibrium problems...

inverse-strongly monotone operator | Mathematical and Computational Biology | Analysis | a system of generalized mixed equilibrium problem | Mathematics, general | modified block iterative algorithm | Mathematics | variational inequality | Topology | Applications of Mathematics | uniformly quasi- ϕ -asymptotically nonexpansive mapping | Differential Geometry | Modified block iterative algorithm | Inverse-strongly monotone operator | A system of generalized mixed equilibrium problem | Variational inequality | Uniformly quasi-φ-asymptotically nonexpansive mapping | uniformly quasi-ϕ-asymptotically nonexpansive mapping

inverse-strongly monotone operator | Mathematical and Computational Biology | Analysis | a system of generalized mixed equilibrium problem | Mathematics, general | modified block iterative algorithm | Mathematics | variational inequality | Topology | Applications of Mathematics | uniformly quasi- ϕ -asymptotically nonexpansive mapping | Differential Geometry | Modified block iterative algorithm | Inverse-strongly monotone operator | A system of generalized mixed equilibrium problem | Variational inequality | Uniformly quasi-φ-asymptotically nonexpansive mapping | uniformly quasi-ϕ-asymptotically nonexpansive mapping

Journal Article

Journal of global optimization, ISSN 1573-2916, 2018, Volume 72, Issue 3, pp. 553 - 577

...” mappings associated to the original object that one aims to optimize. In this paper we abstract from the corresponding resolvents employed in these problems the natural notion of jointly firmly nonexpansive families of mappings...

Jointly firmly nonexpansive families | Uniformly firmly nonexpansive mappings | Mathematics | Proximal point algorithm | Optimization | CAT spaces | Convex optimization | Rates of convergence | 90C25 | Operations Research/Decision Theory | Proof mining | 47H09 | Computer Science, general | 47J25 | 46N10 | 03F10 | Real Functions | MATHEMATICS, APPLIED | HARMONIC MAPS | METRIC-SPACES | GEODESIC SPACES | ASYMPTOTIC-BEHAVIOR | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | FUNCTIONAL-ANALYSIS | FIRMLY NONEXPANSIVE-MAPPINGS | LOGICAL METATHEOREMS | FIXED-POINTS | MONOTONE-OPERATORS | Computer science | Mineral industry | Algorithms | Numerical analysis | Mining industry | Analysis | Computational geometry | Fixed points (mathematics) | Hilbert space | Convexity | Data mining | Convex analysis | Convergence

Jointly firmly nonexpansive families | Uniformly firmly nonexpansive mappings | Mathematics | Proximal point algorithm | Optimization | CAT spaces | Convex optimization | Rates of convergence | 90C25 | Operations Research/Decision Theory | Proof mining | 47H09 | Computer Science, general | 47J25 | 46N10 | 03F10 | Real Functions | MATHEMATICS, APPLIED | HARMONIC MAPS | METRIC-SPACES | GEODESIC SPACES | ASYMPTOTIC-BEHAVIOR | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | FUNCTIONAL-ANALYSIS | FIRMLY NONEXPANSIVE-MAPPINGS | LOGICAL METATHEOREMS | FIXED-POINTS | MONOTONE-OPERATORS | Computer science | Mineral industry | Algorithms | Numerical analysis | Mining industry | Analysis | Computational geometry | Fixed points (mathematics) | Hilbert space | Convexity | Data mining | Convex analysis | Convergence

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 10

...; uniformly convex Banach space; uniformly convex in every direction (UCED); λ-ﬁrmly nonexpansive mapping; asymptotic radius; asymptotic center; (UAC)-property; reactive...

uniformly convex Banach space | asymptotic center | λ -firmly nonexpansive mapping | Mathematics | Smarzewski’s fixed point theorem | asymptotic radius | uniformly convex in every direction | reactive firmly nonexpansive mapping | Analysis | property | Mathematics, general | strictly convex Banach space | Applications of Mathematics | uniformly convex in every direction [InlineEquation not available: see fulltext.] | [InlineEquation not available: see fulltext.]-property | λ-firmly nonexpansive mapping | MATHEMATICS, APPLIED | SPACES | lambda-firmly nonexpansive mapping | MATHEMATICS | uniformly convex in every direction (UCED) | MAPPINGS | (UAC)-property | Smarzewski's fixed point theorem | Theorems | Fixed points (mathematics) | Inequalities

uniformly convex Banach space | asymptotic center | λ -firmly nonexpansive mapping | Mathematics | Smarzewski’s fixed point theorem | asymptotic radius | uniformly convex in every direction | reactive firmly nonexpansive mapping | Analysis | property | Mathematics, general | strictly convex Banach space | Applications of Mathematics | uniformly convex in every direction [InlineEquation not available: see fulltext.] | [InlineEquation not available: see fulltext.]-property | λ-firmly nonexpansive mapping | MATHEMATICS, APPLIED | SPACES | lambda-firmly nonexpansive mapping | MATHEMATICS | uniformly convex in every direction (UCED) | MAPPINGS | (UAC)-property | Smarzewski's fixed point theorem | Theorems | Fixed points (mathematics) | Inequalities

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 71, Issue 10, pp. 4500 - 4506

The main aim of this paper is to study the strong convergence of Halpern iteration for firmly type nonexpansive mappings defined on a Banach space with a uniformly...

Firmly type nonexpansive mappings | Halpern iteration | Uniformly Gâteaux differentiable norm | MATHEMATICS | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | APPROXIMATION | BANACH-SPACES | STRONG-CONVERGENCE THEOREMS | ALGORITHMS | OPERATORS | FIXED-POINTS

Firmly type nonexpansive mappings | Halpern iteration | Uniformly Gâteaux differentiable norm | MATHEMATICS | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | APPROXIMATION | BANACH-SPACES | STRONG-CONVERGENCE THEOREMS | ALGORITHMS | OPERATORS | FIXED-POINTS

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2017, Volume 2017, Issue 1, pp. 1 - 12

The aim of this paper is to introduce a viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth spaces...

nonexpansive mapping | uniformly smooth Banach space | strong convergence | implicit midpoint rule | STRICT PSEUDO-CONTRACTIONS | APPROXIMATION METHODS | MATHEMATICS, APPLIED | GENERAL SYSTEM | 2-UNIFORMLY SMOOTH | FAMILY | VARIATIONAL-INEQUALITIES | MATHEMATICS | CONVERGENCE THEOREMS | ORDINARY DIFFERENTIAL-EQUATIONS | FIXED-POINTS | Viscosity | Iterative algorithms | Error analysis | Banach spaces | Iterative methods | 47H10 | 47J20 | Research | 49H09

nonexpansive mapping | uniformly smooth Banach space | strong convergence | implicit midpoint rule | STRICT PSEUDO-CONTRACTIONS | APPROXIMATION METHODS | MATHEMATICS, APPLIED | GENERAL SYSTEM | 2-UNIFORMLY SMOOTH | FAMILY | VARIATIONAL-INEQUALITIES | MATHEMATICS | CONVERGENCE THEOREMS | ORDINARY DIFFERENTIAL-EQUATIONS | FIXED-POINTS | Viscosity | Iterative algorithms | Error analysis | Banach spaces | Iterative methods | 47H10 | 47J20 | Research | 49H09

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2008, Volume 47, Issue 4, pp. 2096 - 2136

In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a...

firm operator | inverse strongly monotone operator | nonexpansivity pole | antiresolvent | Bregman distance | resolvent | nonexpansive operator | Bregman projection | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | relative projection | uniformly convex function | APPROXIMATIONS | D-f-firm operator | D-f-nonexpansive operator | proximal point method | REFLEXIVE BANACH-SPACES | maximal monotone operator | Tikhonov-Browder regularization | D-f-antiresolvent | WEAK-CONVERGENCE | firmly nonexpansive operator | D-f-resolvent | projected subgradient method | AUTOMATION & CONTROL SYSTEMS | sequentially consistent function | proximal projection method | D-f-nonexpansivity pole | variational inequality | MONOTONE OPERATORS | ALGORITHMS | monotone operator | strongly monotone operator | VARIATIONAL-INEQUALITIES | proximal mapping | POINT METHOD | ANALYSE FONCTIONNELLE | Legendre function | OPTIMIZATION | D-f-inverse strongly monotone operator

firm operator | inverse strongly monotone operator | nonexpansivity pole | antiresolvent | Bregman distance | resolvent | nonexpansive operator | Bregman projection | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | relative projection | uniformly convex function | APPROXIMATIONS | D-f-firm operator | D-f-nonexpansive operator | proximal point method | REFLEXIVE BANACH-SPACES | maximal monotone operator | Tikhonov-Browder regularization | D-f-antiresolvent | WEAK-CONVERGENCE | firmly nonexpansive operator | D-f-resolvent | projected subgradient method | AUTOMATION & CONTROL SYSTEMS | sequentially consistent function | proximal projection method | D-f-nonexpansivity pole | variational inequality | MONOTONE OPERATORS | ALGORITHMS | monotone operator | strongly monotone operator | VARIATIONAL-INEQUALITIES | proximal mapping | POINT METHOD | ANALYSE FONCTIONNELLE | Legendre function | OPTIMIZATION | D-f-inverse strongly monotone operator

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 7/2019, Volume 113, Issue 3, pp. 2017 - 2035

... -nonexpansive mappings in strictly convex and uniformly smooth Banach spaces. A numerical example is given to illustrate the convergence of the proposed hybrid projection...

Strictly convex and uniformly smooth Banach space | 47H10 | Theoretical, Mathematical and Computational Physics | Asymptotically quasi $$\phi $$ ϕ -nonexpansive mapping | Primary 47H09 | Mathematics, general | Mathematics | Applications of Mathematics | Secondary 47J25 | 65J15 | Hybird projection algorithm

Strictly convex and uniformly smooth Banach space | 47H10 | Theoretical, Mathematical and Computational Physics | Asymptotically quasi $$\phi $$ ϕ -nonexpansive mapping | Primary 47H09 | Mathematics, general | Mathematics | Applications of Mathematics | Secondary 47J25 | 65J15 | Hybird projection algorithm

Journal Article

SpringerPlus, ISSN 2193-1801, 12/2012, Volume 1, Issue 1, pp. 1 - 14

...- asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α...

A system of equilibrium problem | Uniformly quasi- ϕ -asymptotically nonexpansive mapping | 47H10 | Hybrid block iterative algorithm | Variational inequality | 47H09 | Inverse-strongly monotone operator | 47H05 | Science, general | MULTIDISCIPLINARY SCIENCES | COUNTABLE FAMILY | STRONG-CONVERGENCE THEOREMS | Uniformly quasi-phi-asymptotically nonexpansive mapping | WEAK-CONVERGENCE | PROJECTION METHOD | OPERATORS | RELATIVELY NONEXPANSIVE-MAPPINGS | FIXED-POINT PROBLEMS

A system of equilibrium problem | Uniformly quasi- ϕ -asymptotically nonexpansive mapping | 47H10 | Hybrid block iterative algorithm | Variational inequality | 47H09 | Inverse-strongly monotone operator | 47H05 | Science, general | MULTIDISCIPLINARY SCIENCES | COUNTABLE FAMILY | STRONG-CONVERGENCE THEOREMS | Uniformly quasi-phi-asymptotically nonexpansive mapping | WEAK-CONVERGENCE | PROJECTION METHOD | OPERATORS | RELATIVELY NONEXPANSIVE-MAPPINGS | FIXED-POINT PROBLEMS

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 2/2011, Volume 15, Issue 1, pp. 259 - 281

.... : Convex function, Firmly nonexpansive-type mapping, Fixed point, Minimization, Monotone operator, Proximal point algorithm, Uniformly convex Banach space, Zero point.

Hilbert spaces | Mathematical theorems | Banach space | Perceptron convergence procedure | Firmly nonexpansive-type mapping | Minimization | Uniformly convex banach space | Convex function | Monotone operator | Proximal point algorithm | Zero point | Fixed point | APPROXIMATION | ALGORITHM | STRONG-CONVERGENCE THEOREMS | Uniformly convex Banach space | FAMILY | WEAK | MATHEMATICS | RELATIVELY NONEXPANSIVE-MAPPINGS | FIXED-POINTS

Hilbert spaces | Mathematical theorems | Banach space | Perceptron convergence procedure | Firmly nonexpansive-type mapping | Minimization | Uniformly convex banach space | Convex function | Monotone operator | Proximal point algorithm | Zero point | Fixed point | APPROXIMATION | ALGORITHM | STRONG-CONVERGENCE THEOREMS | Uniformly convex Banach space | FAMILY | WEAK | MATHEMATICS | RELATIVELY NONEXPANSIVE-MAPPINGS | FIXED-POINTS

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2011, Volume 2011, Issue 1, pp. 1 - 20

...-asymptotically nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, and the set of solutions of the generalized equilibrium problems...

inverse-strongly monotone operator | generalized equilibrium problem | Analysis | Mathematics, general | Mathematics | variational inequality | Applications of Mathematics | uniformly quasi- ϕ -asymptotically nonexpansive mapping | iterative algorithms | Inverse-strongly monotone operator | Iterative algorithms | Variational inequality | Uniformly quasi-φ-asymptotically nonexpansive mapping | Generalized equilibrium problem

inverse-strongly monotone operator | generalized equilibrium problem | Analysis | Mathematics, general | Mathematics | variational inequality | Applications of Mathematics | uniformly quasi- ϕ -asymptotically nonexpansive mapping | iterative algorithms | Inverse-strongly monotone operator | Iterative algorithms | Variational inequality | Uniformly quasi-φ-asymptotically nonexpansive mapping | Generalized equilibrium problem

Journal Article

Numerical algorithms, ISSN 1572-9265, 2015, Volume 72, Issue 4, pp. 835 - 864

The purpose of this paper is to study split feasibility problems and fixed point problems concerning left Bregman strongly relatively nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces...

Strong convergence | Uniformly smooth | Numeric Computing | Theory of Computation | Left Bregman strongly nonexpansive mappings | Split feasibility problem | Fixed point problem | Algorithms | Algebra | 49J53 | 90C25 | Numerical Analysis | Computer Science | 65K10 | 49M37 | Uniformly convex | PROJECTION | MATHEMATICS, APPLIED | NONEXPANSIVE OPERATORS | THEOREMS | SETS | CQ ALGORITHM

Strong convergence | Uniformly smooth | Numeric Computing | Theory of Computation | Left Bregman strongly nonexpansive mappings | Split feasibility problem | Fixed point problem | Algorithms | Algebra | 49J53 | 90C25 | Numerical Analysis | Computer Science | 65K10 | 49M37 | Uniformly convex | PROJECTION | MATHEMATICS, APPLIED | NONEXPANSIVE OPERATORS | THEOREMS | SETS | CQ ALGORITHM

Journal Article

15.
Shrinking projection algorithm for fixed points of firmly nonexpansive mappings and its applications

Fixed Point Theory, ISSN 1583-5022, 2010, Volume 11, Issue 2, pp. 301 - 310

The purpose of this paper is to study. the shrinking projection method for finding common fixed points of firmly nonexpansive mappings...

Shrinking projection method | Uniformly closed | Equilibrium problem | Firmly nonexpansive mapping | firmly nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | ITERATIONS | uniformly closed | equilibrium problem | STRONG-CONVERGENCE THEOREMS | OPERATORS | FAMILY

Shrinking projection method | Uniformly closed | Equilibrium problem | Firmly nonexpansive mapping | firmly nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | ITERATIONS | uniformly closed | equilibrium problem | STRONG-CONVERGENCE THEOREMS | OPERATORS | FAMILY

Journal Article

Journal of fixed point theory and applications, ISSN 1661-7746, 2018, Volume 20, Issue 1, pp. 1 - 17

The purpose of this paper is to propose and study an algorithm for solving the general split equality problem governed by Bregman quasi-nonexpansive mappings in Banach spaces...

duality mapping | Mathematics | uniformly smooth | strong convergence | uniformly convex | Mathematical Methods in Physics | 49J53 | Analysis | 47H09 | Mathematics, general | 65K10 | general split problems | 49M37 | 47H05 | Bregman quasi-nonexpansive mappings | FIXED-POINT PROBLEM | MATHEMATICS, APPLIED | STRONG-CONVERGENCE THEOREMS | ALGORITHMS | MATHEMATICS | CONVEX | EQUILIBRIUM | ITERATIVE METHODS | Algorithms | Equality

duality mapping | Mathematics | uniformly smooth | strong convergence | uniformly convex | Mathematical Methods in Physics | 49J53 | Analysis | 47H09 | Mathematics, general | 65K10 | general split problems | 49M37 | 47H05 | Bregman quasi-nonexpansive mappings | FIXED-POINT PROBLEM | MATHEMATICS, APPLIED | STRONG-CONVERGENCE THEOREMS | ALGORITHMS | MATHEMATICS | CONVEX | EQUILIBRIUM | ITERATIVE METHODS | Algorithms | Equality

Journal Article

17.
Full Text
Strong convergence of block-iterative outer approximation methods for convex optimization

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2000, Volume 38, Issue 2, pp. 538 - 565

The strong convergence of a broad class of outer approximation methods for minimizing a convex function over the intersection of an arbitrary number of convex...

projection onto an intersection of convex sets | FEASIBILITY PROBLEMS | HILBERT-SPACES | MATHEMATICS, APPLIED | uniformly convex function | PRODUCT SPACE | outer approximation | ALGORITHM | convex programming | reflexive Banach space | surrogate cut | constrained minimization | fixed point | inconsistent constraints | SURROGATE PROJECTION METHODS | SETS | convex feasibility problem | block-iterative | cutting plane | FIRMLY NONEXPANSIVE-MAPPINGS | FIXED-POINTS | AUTOMATION & CONTROL SYSTEMS

projection onto an intersection of convex sets | FEASIBILITY PROBLEMS | HILBERT-SPACES | MATHEMATICS, APPLIED | uniformly convex function | PRODUCT SPACE | outer approximation | ALGORITHM | convex programming | reflexive Banach space | surrogate cut | constrained minimization | fixed point | inconsistent constraints | SURROGATE PROJECTION METHODS | SETS | convex feasibility problem | block-iterative | cutting plane | FIRMLY NONEXPANSIVE-MAPPINGS | FIXED-POINTS | AUTOMATION & CONTROL SYSTEMS

Journal Article

Numerical functional analysis and optimization, ISSN 1532-2467, 2013, Volume 34, Issue 10, pp. 1129 - 1155

In this article, using Bregman functions, we first introduce new modified Mann and Halpern's iterations for finding common fixed points of an infinite family of Bregman relatively nonexpansive...

Bregman relatively nonexpansive mapping | Strong convergence | Uniformly smooth function | Uniformly convex function | Bregman function | Fixed point | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | 37C25 | WEAK | NONLINEAR MAPPINGS | 47H10 | FIXED-POINT THEOREMS | STRONG-CONVERGENCE | Approximation

Bregman relatively nonexpansive mapping | Strong convergence | Uniformly smooth function | Uniformly convex function | Bregman function | Fixed point | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | 37C25 | WEAK | NONLINEAR MAPPINGS | 47H10 | FIXED-POINT THEOREMS | STRONG-CONVERGENCE | Approximation

Journal Article

Ricerche di Matematica, ISSN 0035-5038, 6/2016, Volume 65, Issue 1, pp. 209 - 220

In this paper, we introduce a new iteration process for solving fixed point problem of Bregman strongly nonexpansive mappings, and then we study a strong convergence theorem for a common fixed point...

Strongly Convergence | Probability Theory and Stochastic Processes | Mathematics | Uniformly Frèchet differentiable | 54H25 | Geometry | 47H10 | Algebra | Bregman strongly nonexpansive mapping | Common fixed point | Analysis | Numerical Analysis | Mathematics, general

Strongly Convergence | Probability Theory and Stochastic Processes | Mathematics | Uniformly Frèchet differentiable | 54H25 | Geometry | 47H10 | Algebra | Bregman strongly nonexpansive mapping | Common fixed point | Analysis | Numerical Analysis | Mathematics, general

Journal Article

Journal of the Korean Mathematical Society, ISSN 0304-9914, 2008, Volume 45, Issue 2, pp. 377 - 392

... A. As an application, we give strong convergence of the path {x(t)} defined by x(t) = tAx(t) + (1 - t) (2I - T)x(t) to a fixed point of firmly pseudo contractive mapping T.

Uniformly Gateaux differentiable norm | Pseudocontractive mapping | Variational inequality | Fixed points | Firmly pseudocontractive mapping | Strongly pseudocontractive mapping | Nonexpansive mapping | MATHEMATICS, APPLIED | pseudo contractive mapping | fixed points | nonexpansive mapping | ACCRETIVE-OPERATORS | variational inequality | MATHEMATICS | firmly pseudocontractive mapping | THEOREMS | strongly pseudocontractive mapping | uniformly Gateaux differentiable norm | NONEXPANSIVE NONSELF-MAPPINGS | PSEUDO-CONTRACTIVE MAPPINGS | FIXED-POINTS

Uniformly Gateaux differentiable norm | Pseudocontractive mapping | Variational inequality | Fixed points | Firmly pseudocontractive mapping | Strongly pseudocontractive mapping | Nonexpansive mapping | MATHEMATICS, APPLIED | pseudo contractive mapping | fixed points | nonexpansive mapping | ACCRETIVE-OPERATORS | variational inequality | MATHEMATICS | firmly pseudocontractive mapping | THEOREMS | strongly pseudocontractive mapping | uniformly Gateaux differentiable norm | NONEXPANSIVE NONSELF-MAPPINGS | PSEUDO-CONTRACTIVE MAPPINGS | FIXED-POINTS

Journal Article

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