Mathematical programming, ISSN 1436-4646, 2018, Volume 170, Issue 1, pp. 177 - 206

Several aspects of the interplay between monotone operator theory and convex optimization are presented...

65K05 | Self-dual class | Theoretical, Mathematical and Computational Physics | Subdifferential | Proximity operator | Mathematics | Monotone operator | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Proximal algorithm | Operator splitting | Proximity-preserving transformation | 49M27 | Combinatorics | Firmly nonexpansive operator | 47H25 | MATHEMATICS, APPLIED | SIGNAL RECOVERY | THRESHOLDING ALGORITHM | DECOMPOSITION | PROXIMAL POINT ALGORITHM | LEAST-SQUARES SOLUTIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | NONLINEAR OPERATORS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ANALYSE FONCTIONNELLE | CONVERGENCE | PARTIAL INVERSES | SPLITTING METHOD | Analysis | Algorithms | Computational geometry | Operators | Proximity | Convexity | Convex analysis | Optimization

65K05 | Self-dual class | Theoretical, Mathematical and Computational Physics | Subdifferential | Proximity operator | Mathematics | Monotone operator | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Proximal algorithm | Operator splitting | Proximity-preserving transformation | 49M27 | Combinatorics | Firmly nonexpansive operator | 47H25 | MATHEMATICS, APPLIED | SIGNAL RECOVERY | THRESHOLDING ALGORITHM | DECOMPOSITION | PROXIMAL POINT ALGORITHM | LEAST-SQUARES SOLUTIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | NONLINEAR OPERATORS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ANALYSE FONCTIONNELLE | CONVERGENCE | PARTIAL INVERSES | SPLITTING METHOD | Analysis | Algorithms | Computational geometry | Operators | Proximity | Convexity | Convex analysis | Optimization

Journal Article

Journal of scientific computing, ISSN 1573-7691, 2018, Volume 76, Issue 3, pp. 1698 - 1717

... {A}}$$ A is a bounded linear operator. The proposed algorithm has some famous primal–dual algorithms for minimizing the sum of two functions as special cases. E.g...

Computational Mathematics and Numerical Analysis | Nonexpansive operator | Algorithms | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Three-operator splitting | Chambolle–Pock | Mathematics | Fixed-point iteration | Primal–dual | MATHEMATICS, APPLIED | Chambolle-Pock | Primal-dual | CONVERGENCE RATE ANALYSIS | OPTIMIZATION | SPLITTING SCHEMES | SOLVING MONOTONE INCLUSIONS

Computational Mathematics and Numerical Analysis | Nonexpansive operator | Algorithms | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Three-operator splitting | Chambolle–Pock | Mathematics | Fixed-point iteration | Primal–dual | MATHEMATICS, APPLIED | Chambolle-Pock | Primal-dual | CONVERGENCE RATE ANALYSIS | OPTIMIZATION | SPLITTING SCHEMES | SOLVING MONOTONE INCLUSIONS

Journal Article

Mathematics of operations research, ISSN 1526-5471, 2016, Volume 41, Issue 3, pp. 884 - 897

The problem of finding a minimizer of the sum of two convex functions—or, more generally, that of finding a zero of the sum of two maximally monotone operators...

firmly nonexpansive mapping | displacement mapping | near equality | subdifferential operator | convex function | nearly convex set | range | normal problem | Douglas–Rachford splitting operator | Brezis–Haraux theorem | maximally monotone operator | Attouch–Théra duality | Brezis-Haraux theorem | Maximally monotone operator | Near equality | Normal problem | Douglas-Rachford splitting operator | Nearly convex set | Firmly nonexpansive mapping | Subdifferential operator | Attouch-thera duality | Displacement mapping | Convex function | Range | MATHEMATICS, APPLIED | Attouch-Thera duality | SUM | PARAMONOTONICITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DUALITY | MONOTONE-OPERATORS | Transformations (Mathematics) | Analysis | Convex functions

firmly nonexpansive mapping | displacement mapping | near equality | subdifferential operator | convex function | nearly convex set | range | normal problem | Douglas–Rachford splitting operator | Brezis–Haraux theorem | maximally monotone operator | Attouch–Théra duality | Brezis-Haraux theorem | Maximally monotone operator | Near equality | Normal problem | Douglas-Rachford splitting operator | Nearly convex set | Firmly nonexpansive mapping | Subdifferential operator | Attouch-thera duality | Displacement mapping | Convex function | Range | MATHEMATICS, APPLIED | Attouch-Thera duality | SUM | PARAMONOTONICITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DUALITY | MONOTONE-OPERATORS | Transformations (Mathematics) | Analysis | Convex functions

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 reflexive Banach space...

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

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

Journal Article

Journal of approximation theory, ISSN 0021-9045, 2012, Volume 164, Issue 8, pp. 1065 - 1084

The problem of finding the zeros of the sum of two maximally monotone operators is of fundamental importance in optimization and variational analysis...

Subdifferential operator | Fenchel duality | Douglas–Rachford splitting | Maximal monotone operator | Total duality | Nonexpansive mapping | Resolvent | Fenchel–Rockafellar duality | Paramonotonicity | Firmly nonexpansive mapping | Hilbert space | Eckstein–Ferris–Pennanen–Robinson duality | Attouch–Théra duality | Fixed point | Eckstein-Ferris-Pennanen-Robinson duality | Douglas-Rachford splitting | Attouch-Théra duality | Fenchel-Rockafellar duality | APPROXIMATION | Attouch-Thera duality | FITZPATRICK FUNCTIONS | MATHEMATICS | MAXIMAL MONOTONE-OPERATORS | VARIATIONAL INEQUALITY PROBLEM | PROXIMAL POINT ALGORITHM | CLOSED CONVEX-SETS | LAGRANGE DUALITY | PARALLEL SUM | HILBERT-SPACE | FIXED-POINTS

Subdifferential operator | Fenchel duality | Douglas–Rachford splitting | Maximal monotone operator | Total duality | Nonexpansive mapping | Resolvent | Fenchel–Rockafellar duality | Paramonotonicity | Firmly nonexpansive mapping | Hilbert space | Eckstein–Ferris–Pennanen–Robinson duality | Attouch–Théra duality | Fixed point | Eckstein-Ferris-Pennanen-Robinson duality | Douglas-Rachford splitting | Attouch-Théra duality | Fenchel-Rockafellar duality | APPROXIMATION | Attouch-Thera duality | FITZPATRICK FUNCTIONS | MATHEMATICS | MAXIMAL MONOTONE-OPERATORS | VARIATIONAL INEQUALITY PROBLEM | PROXIMAL POINT ALGORITHM | CLOSED CONVEX-SETS | LAGRANGE DUALITY | PARALLEL SUM | HILBERT-SPACE | FIXED-POINTS

Journal Article

Mathematical Programming, ISSN 0025-5610, 3/2018, Volume 168, Issue 1, pp. 55 - 61

The problem of finding a zero of the sum of two maximally monotone operators is of central importance in optimization...

Theoretical, Mathematical and Computational Physics | Primary 47H09 | Proximal mapping | Mathematics | Nowhere dense set | Maximally monotone operator | Mathematical Methods in Physics | Resolvent | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Firmly nonexpansive mapping | Douglas–Rachford algorithm | Combinatorics | Secondary 47H05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | POINT ALGORITHM | Algorithms | Operators | Mapping

Theoretical, Mathematical and Computational Physics | Primary 47H09 | Proximal mapping | Mathematics | Nowhere dense set | Maximally monotone operator | Mathematical Methods in Physics | Resolvent | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Firmly nonexpansive mapping | Douglas–Rachford algorithm | Combinatorics | Secondary 47H05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | POINT ALGORITHM | Algorithms | Operators | Mapping

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2014, Volume 2014, Issue 1, pp. 1 - 15

In this paper, we investigate a splitting algorithm for treating monotone operators...

maximal monotone operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | Topology | Differential Geometry | proximal point algorithm | Maximal monotone operator | Proximal point algorithm | Zero point | Nonexpansive mapping | Fixed point | APPROXIMATION | ITERATIVE ALGORITHM | MATHEMATICS | SEMIGROUPS | THEOREMS | MAPPINGS | ZERO POINTS | EQUILIBRIUM PROBLEMS | FIXED-POINTS | Fixed point theory | Usage | Hilbert space | Contraction operators | Operators | Theorems | Splitting | Algorithms | Convergence

maximal monotone operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | Topology | Differential Geometry | proximal point algorithm | Maximal monotone operator | Proximal point algorithm | Zero point | Nonexpansive mapping | Fixed point | APPROXIMATION | ITERATIVE ALGORITHM | MATHEMATICS | SEMIGROUPS | THEOREMS | MAPPINGS | ZERO POINTS | EQUILIBRIUM PROBLEMS | FIXED-POINTS | Fixed point theory | Usage | Hilbert space | Contraction operators | Operators | Theorems | Splitting | Algorithms | Convergence

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2015, Volume 425, Issue 1, pp. 55 - 70

Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces...

Averaged operator | Nonexpansive operator | Monotone operator | Fixed-point algorithm | Forward–backward splitting | Forward-backward splitting | MATHEMATICS | MATHEMATICS, APPLIED | MONOTONE INCLUSIONS | FIXED-POINT SET | ITERATIVE ALGORITHMS | Algorithms

Averaged operator | Nonexpansive operator | Monotone operator | Fixed-point algorithm | Forward–backward splitting | Forward-backward splitting | MATHEMATICS | MATHEMATICS, APPLIED | MONOTONE INCLUSIONS | FIXED-POINT SET | ITERATIVE ALGORITHMS | Algorithms

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 2180-4206, 2017, Volume 42, Issue 1, pp. 105 - 118

... are mathematically modeled as a nonlinear operator equation and this operator is decomposed as the sum of two (possibly simpler...

MSC 47H09 | Mathematics, general | Mathematics | Maximal monotone operator | Applications of Mathematics | MSC 47H10 | Banach space | Splitting method | Accretive operator | Forward–backward algorithm | MATHEMATICS | NONEXPANSIVE-MAPPINGS | MAXIMAL MONOTONE-OPERATORS | SUM | STRONG-CONVERGENCE THEOREMS | ALGORITHMS | Forward-backward algorithm

MSC 47H09 | Mathematics, general | Mathematics | Maximal monotone operator | Applications of Mathematics | MSC 47H10 | Banach space | Splitting method | Accretive operator | Forward–backward algorithm | MATHEMATICS | NONEXPANSIVE-MAPPINGS | MAXIMAL MONOTONE-OPERATORS | SUM | STRONG-CONVERGENCE THEOREMS | ALGORITHMS | Forward-backward algorithm

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2015, Volume 2015, Issue 1, pp. 1 - 19

The split common fixed point problem for two quasi-pseudo-contractive operators is studied...

Mathematical and Computational Biology | Mathematics | Topology | directed operator | quasi-pseudo-contractive operator | 90C25 | Analysis | demicontractive operator | 47H09 | Mathematics, general | split common fixed point problem | Applications of Mathematics | Differential Geometry | 47J25 | quasi-nonexpansive operator | 65J15 | HILBERT-SPACES | MATHEMATICS, APPLIED | METRIC-SPACES | ITERATIVE ALGORITHMS | WEAK | MATHEMATICS | BANACH-SPACES | MAPPINGS | STRONG-CONVERGENCE | Fixed point theory | Usage | Convergence (Mathematics) | Algorithms | Operator theory | Operators | Construction | Theorems | Fixed points (mathematics) | Iterative algorithms | Convergence

Mathematical and Computational Biology | Mathematics | Topology | directed operator | quasi-pseudo-contractive operator | 90C25 | Analysis | demicontractive operator | 47H09 | Mathematics, general | split common fixed point problem | Applications of Mathematics | Differential Geometry | 47J25 | quasi-nonexpansive operator | 65J15 | HILBERT-SPACES | MATHEMATICS, APPLIED | METRIC-SPACES | ITERATIVE ALGORITHMS | WEAK | MATHEMATICS | BANACH-SPACES | MAPPINGS | STRONG-CONVERGENCE | Fixed point theory | Usage | Convergence (Mathematics) | Algorithms | Operator theory | Operators | Construction | Theorems | Fixed points (mathematics) | Iterative algorithms | Convergence

Journal Article

Nonlinear analysis, ISSN 0362-546X, 2012, Volume 75, Issue 14, pp. 5448 - 5465

We introduce and study new classes of Bregman nonexpansive operators in reflexive Banach spaces...

Boltzmann–Shannon entropy | Bregman firmly nonexpansive operator | Nonexpansive operator | Reflexive Banach space | Resolvent | Retraction | Monotone mapping | [formula omitted]-monotone mapping | Legendre function | Bregman distance | Totally convex function | Fermi–Dirac entropy | T-monotone mapping | Fermi-Dirac entropy | Boltzmann-Shannon entropy | MATHEMATICS, APPLIED | ALGORITHM | MATHEMATICS | MAPPINGS | PROJECTIONS

Boltzmann–Shannon entropy | Bregman firmly nonexpansive operator | Nonexpansive operator | Reflexive Banach space | Resolvent | Retraction | Monotone mapping | [formula omitted]-monotone mapping | Legendre function | Bregman distance | Totally convex function | Fermi–Dirac entropy | T-monotone mapping | Fermi-Dirac entropy | Boltzmann-Shannon entropy | MATHEMATICS, APPLIED | ALGORITHM | MATHEMATICS | MAPPINGS | PROJECTIONS

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2015, Volume 421, Issue 1, pp. 1 - 20

We introduce regularity notions for averaged nonexpansive operators. Combined with regularity notions of their fixed point sets, we obtain linear and strong convergence results for quasicyclic, cyclic, and random iterations...

Douglas–Rachford algorithm | Averaged nonexpansive mapping | Projection | Nonexpansive operator | Convex feasibility problem | Bounded linear regularity | Douglas-Rachford algorithm | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | PROJECTIONS | Analysis | Algorithms

Douglas–Rachford algorithm | Averaged nonexpansive mapping | Projection | Nonexpansive operator | Convex feasibility problem | Bounded linear regularity | Douglas-Rachford algorithm | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | PROJECTIONS | Analysis | Algorithms

Journal Article

Analele Universitatii "Ovidius" Constanta - Seria Matematica, ISSN 1224-1784, 12/2019, Volume 27, Issue 3, pp. 153 - 175

In this paper, we study the split common fixed point problem in Hilbert spaces. We find a common solution of the split common fixed point problem for two demicontractive operators without knowledge of operator norms...

split feasibility problem | Secondary 49M05 | demicontractive operator | Primary 47H09 | split common fixed point problem | common solution | Hilbert space | NONEXPANSIVE MULTIVALUED MAPPINGS | MATHEMATICS, APPLIED | HYBRID PAIR | ITERATIVE METHOD | FAMILY | MATHEMATICS | PROJECTION | SETS | COMMON FIXED-POINT

split feasibility problem | Secondary 49M05 | demicontractive operator | Primary 47H09 | split common fixed point problem | common solution | Hilbert space | NONEXPANSIVE MULTIVALUED MAPPINGS | MATHEMATICS, APPLIED | HYBRID PAIR | ITERATIVE METHOD | FAMILY | MATHEMATICS | PROJECTION | SETS | COMMON FIXED-POINT

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2013, Volume 2013, Issue 1, pp. 199 - 14

In this paper, an iterative algorithm is proposed to study some nonlinear operators which are inverse-strongly monotone, maximal monotone, and strictly pseudocontractive...

maximal monotone operator | strictly pseudocontractive mapping | inverse-strongly monotone mapping | fixed point | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | resolvent | Inverse-strongly monotone mapping | Maximal monotone operator | Strictly pseudocontractive mapping | Resolvent | Fixed point | COMMON SOLUTIONS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | MATHEMATICS | HYBRID PROJECTION METHODS | THEOREMS | WEAK-CONVERGENCE | SEQUENCE | EQUILIBRIUM PROBLEMS | FIXED-POINT PROBLEMS

maximal monotone operator | strictly pseudocontractive mapping | inverse-strongly monotone mapping | fixed point | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | resolvent | Inverse-strongly monotone mapping | Maximal monotone operator | Strictly pseudocontractive mapping | Resolvent | Fixed point | COMMON SOLUTIONS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | MATHEMATICS | HYBRID PROJECTION METHODS | THEOREMS | WEAK-CONVERGENCE | SEQUENCE | EQUILIBRIUM PROBLEMS | FIXED-POINT PROBLEMS

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2013, Volume 400, Issue 2, pp. 597 - 614

We present a detailed study of right and left Bregman strongly nonexpansive operators in reflexive Banach spaces...

Nonexpansive operator | Reflexive Banach space | Resolvent | Monotone mapping | Bregman strongly nonexpansive operator | Legendre function | Bregman distance | Totally convex function | MATHEMATICS, APPLIED | CONVEXITY | DISTANCES | CONVERGENCE THEOREM | MATHEMATICS | PROJECTIONS

Nonexpansive operator | Reflexive Banach space | Resolvent | Monotone mapping | Bregman strongly nonexpansive operator | Legendre function | Bregman distance | Totally convex function | MATHEMATICS, APPLIED | CONVEXITY | DISTANCES | CONVERGENCE THEOREM | MATHEMATICS | PROJECTIONS

Journal Article

Symmetry (Basel), ISSN 2073-8994, 2018, Volume 10, Issue 11, p. 563

The three-operator splitting algorithm is a new splitting algorithm for finding monotone inclusion problems of the sum of three maximally monotone operators, where one is cocoercive...

Inexact three-operator splitting algorithm | Nonexpansive operator | Fixed point | RECOVERY | fixed point | MULTIDISCIPLINARY SCIENCES | PROXIMAL POINT ALGORITHM | OPTIMIZATION | inexact three-operator splitting algorithm | nonexpansive operator | SOLVING MONOTONE INCLUSIONS

Inexact three-operator splitting algorithm | Nonexpansive operator | Fixed point | RECOVERY | fixed point | MULTIDISCIPLINARY SCIENCES | PROXIMAL POINT ALGORITHM | OPTIMIZATION | inexact three-operator splitting algorithm | nonexpansive operator | SOLVING MONOTONE INCLUSIONS

Journal Article

Fixed point theory and applications (Hindawi Publishing Corporation), ISSN 1687-1812, 2014, Volume 2014, Issue 1, pp. 75 - 10

In this paper, a regularization method for treating zero points of the sum of two monotone operators is investigated...

maximal monotone operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | Topology | Differential Geometry | proximal point algorithm | Maximal monotone operator | Proximal point algorithm | Zero point | Nonexpansive mapping | Fixed point | ERRORS | APPROXIMATION | STRONG-CONVERGENCE THEOREMS | ALGORITHMS | MATHEMATICS | ACCRETIVE OPERATOR | MAPPINGS | EQUILIBRIUM PROBLEMS | FIXED-POINTS | Fixed point theory | Usage | Hilbert space | Convergence (Mathematics) | Contraction operators | Operators | Theorems | Regularization | Convergence

maximal monotone operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | Topology | Differential Geometry | proximal point algorithm | Maximal monotone operator | Proximal point algorithm | Zero point | Nonexpansive mapping | Fixed point | ERRORS | APPROXIMATION | STRONG-CONVERGENCE THEOREMS | ALGORITHMS | MATHEMATICS | ACCRETIVE OPERATOR | MAPPINGS | EQUILIBRIUM PROBLEMS | FIXED-POINTS | Fixed point theory | Usage | Hilbert space | Convergence (Mathematics) | Contraction operators | Operators | Theorems | Regularization | Convergence

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2007, Volume 336, Issue 2, pp. 1466 - 1475

The notion of Banach operator pairs is introduced, as a new class of noncommuting maps...

Best approximation | Common fixed-point | Nonexpansive map | Banach operator pair | nonexpansive map | MATHEMATICS | MATHEMATICS, APPLIED | INVARIANT APPROXIMATIONS | common fixed-point | MAPS | best approximation | THEOREMS | banach operator pair | MAPPINGS

Best approximation | Common fixed-point | Nonexpansive map | Banach operator pair | nonexpansive map | MATHEMATICS | MATHEMATICS, APPLIED | INVARIANT APPROXIMATIONS | common fixed-point | MAPS | best approximation | THEOREMS | banach operator pair | MAPPINGS

Journal Article

Fixed point theory and applications (Hindawi Publishing Corporation), ISSN 1687-1812, 2013, Volume 2013, Issue 1, pp. 148 - 17

.... As an application, we consider the problem of finding zeros of m-accretive operators based on an iterative algorithm with errors...

accretive operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | Topology | Differential Geometry | iterative algorithm | Iterative algorithm | Zero point | Accretive operator | Nonexpansive mapping | Fixed point | MATHEMATICS | NONLINEAR MAPPINGS | SEMIGROUPS | STRONG-CONVERGENCE THEOREMS | VISCOSITY APPROXIMATION METHODS | FIXED-POINTS | BANACH | Fixed point theory | Usage | Banach spaces | Contraction operators

accretive operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | Topology | Differential Geometry | iterative algorithm | Iterative algorithm | Zero point | Accretive operator | Nonexpansive mapping | Fixed point | MATHEMATICS | NONLINEAR MAPPINGS | SEMIGROUPS | STRONG-CONVERGENCE THEOREMS | VISCOSITY APPROXIMATION METHODS | FIXED-POINTS | BANACH | Fixed point theory | Usage | Banach spaces | Contraction operators

Journal Article

Abstract and applied analysis, ISSN 1085-3375, 3/2014, Volume 2014

Using Bregman functions, we introduce the new concept of Bregman generalized f -projection operator Proj C f , g : E...

MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | CONVERGENCE THEOREMS | FIXED-POINTS | Inequalities (Mathematics) | Transformations (Mathematics) | Banach spaces | Analysis | Information management | Operators | Gateaux | Banach space | Inequalities

MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | CONVERGENCE THEOREMS | FIXED-POINTS | Inequalities (Mathematics) | Transformations (Mathematics) | Banach spaces | Analysis | Information management | Operators | Gateaux | Banach space | Inequalities

Journal Article