Journal of Applied Analysis, ISSN 1425-6908, 12/2018, Volume 24, Issue 2, pp. 185 - 195

Journal Article

Publ. Mat, 2016, Volume 60, Issue no. 1, pp. 27 - 53

In this paper, we study solutions to a nonlocal 1-Laplacian equation given by ¶ -\int_{\Omega_J}...

45G10 | least gradient functions | 1-Laplacian | 45J05 | median value | 47H06

45G10 | least gradient functions | 1-Laplacian | 45J05 | median value | 47H06

Journal Article

Demonstratio Mathematica, ISSN 2391-4661, 11/2018, Volume 51, Issue 1, pp. 277 - 294

In this paper, we introduce and study the class of demimetric mappings in CAT(0) spaces.We then propose a modified proximal point algorithm for approximating a...

minimization problem | 47H09 | 47J05 | demimetric mappings | 47J25 | fixed point problem | 47H06 | CAT spaces

minimization problem | 47H09 | 47J05 | demimetric mappings | 47J25 | fixed point problem | 47H06 | CAT spaces

Journal Article

Numerical Algorithms, ISSN 1017-1398, 9/2017, Volume 76, Issue 1, pp. 259 - 282

Our aim in this paper is to study strong convergence results for L-Lipschitz continuous monotone variational inequality but L is unknown using a combination of...

Strong convergence | Numeric Computing | Hilbert spaces | Theory of Computation | Subgradient extragradient method | Algorithms | Algebra | Numerical Analysis | Viscosity method | Computer Science | 47H09 | 47J05 | 47J25 | 47H06 | Variational inequalities | EXISTENCE | HILBERT-SPACES | MATHEMATICS, APPLIED | HAMMERSTEIN TYPE | HYBRID METHOD | NONLINEAR INTEGRAL-EQUATIONS | BANACH-SPACES | GRADIENT-METHOD | ITERATIVE APPROXIMATION | OPERATORS

Strong convergence | Numeric Computing | Hilbert spaces | Theory of Computation | Subgradient extragradient method | Algorithms | Algebra | Numerical Analysis | Viscosity method | Computer Science | 47H09 | 47J05 | 47J25 | 47H06 | Variational inequalities | EXISTENCE | HILBERT-SPACES | MATHEMATICS, APPLIED | HAMMERSTEIN TYPE | HYBRID METHOD | NONLINEAR INTEGRAL-EQUATIONS | BANACH-SPACES | GRADIENT-METHOD | ITERATIVE APPROXIMATION | OPERATORS

Journal Article

Advances in Pure and Applied Mathematics, ISSN 1867-1152, 07/2018, Volume 9, Issue 3, pp. 167 - 184

In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is...

convex minimization problem | Legendre functions | Gâteaux differentiable function | Bregman distance | strong convergence | Bregman projection | Fréchet differentiable functions | 47H09 | variational inequality, reflexive Banach space | 47J05 | 47J25 | resolvent | 47H06 | reffexive Banach space | variational inequality | Iterative algorithms | Error analysis | Banach spaces | Banach space | Optimization

convex minimization problem | Legendre functions | Gâteaux differentiable function | Bregman distance | strong convergence | Bregman projection | Fréchet differentiable functions | 47H09 | variational inequality, reflexive Banach space | 47J05 | 47J25 | resolvent | 47H06 | reffexive Banach space | variational inequality | Iterative algorithms | Error analysis | Banach spaces | Banach space | Optimization

Journal Article

Calcolo, ISSN 0008-0624, 12/2018, Volume 55, Issue 4, pp. 1 - 22

In this paper, we introduce two modifications of the forward–backward splitting method with a new step size rule for inclusion problems in real Hilbert spaces....

65K15 | Forward–backward splitting method | 68W10 | Mathematics | Theory of Computation | Mann-type method | 65Y05 | 47H10 | Numerical Analysis | 47H09 | Zero point | Viscosity approximation method | 47H06 | MATHEMATICS | MATHEMATICS, APPLIED | Forward-backward splitting method | CONVERGENCE | SUM | ALGORITHMS | HILBERT-SPACE | MONOTONE-OPERATORS | Methods | Algorithms | Splitting | Hilbert space | Convergence

65K15 | Forward–backward splitting method | 68W10 | Mathematics | Theory of Computation | Mann-type method | 65Y05 | 47H10 | Numerical Analysis | 47H09 | Zero point | Viscosity approximation method | 47H06 | MATHEMATICS | MATHEMATICS, APPLIED | Forward-backward splitting method | CONVERGENCE | SUM | ALGORITHMS | HILBERT-SPACE | MONOTONE-OPERATORS | Methods | Algorithms | Splitting | Hilbert space | Convergence

Journal Article

7.
Full Text
Further Investigation into Split Common Fixed Point Problem for Demicontractive Operators

数学学报：英文版, ISSN 1439-8516, 2016, Volume 32, Issue 11, pp. 1357 - 1376

Our contribution in this paper is to propose an iterative algorithm which does not reqmre prior knowledge of operator norm and prove strong convergence theorem...

split common fixed point problems | Demicontractive mappings | 47H09 | Mathematics, general | Hilbert spaces | Mathematics | 47J05 | iterative scheme | 47J25 | 47H06 | strong convergence | ITERATION | MATHEMATICS, APPLIED | VARIATIONAL INEQUALITY PROBLEM | CYCLIC ALGORITHM | CQ ALGORITHM | MATHEMATICS | PROJECTION | SETS | MAPPINGS | STRONG-CONVERGENCE | Computer science | Investigations | Algorithms | Studies | Mapping | Hilbert space | Mathematical analysis | Approximations | Operators | Fixed points (mathematics) | Norms | Mathematical models | Convergence

split common fixed point problems | Demicontractive mappings | 47H09 | Mathematics, general | Hilbert spaces | Mathematics | 47J05 | iterative scheme | 47J25 | 47H06 | strong convergence | ITERATION | MATHEMATICS, APPLIED | VARIATIONAL INEQUALITY PROBLEM | CYCLIC ALGORITHM | CQ ALGORITHM | MATHEMATICS | PROJECTION | SETS | MAPPINGS | STRONG-CONVERGENCE | Computer science | Investigations | Algorithms | Studies | Mapping | Hilbert space | Mathematical analysis | Approximations | Operators | Fixed points (mathematics) | Norms | Mathematical models | Convergence

Journal Article

Numerical Algorithms, ISSN 1017-1398, 12/2018, Volume 79, Issue 4, pp. 1231 - 1256

In this article, we first propose an extended split equality problem which is an extension of the convex feasibility problem, and then introduce a parameter w...

Numeric Computing | Theory of Computation | Extended split equality problem | Weak convergence | Algorithms | Algebra | Numerical Analysis | Extended split equality fixed point problem | Computer Science | 47H09 | Simultaneous iterative algorithm | 47H05 | 47J25 | 47H06 | Fixed point | EIGENVALUE | MATHEMATICS, APPLIED | CONVEX FEASIBILITY | POLYNOMIAL OPTIMIZATION | HILBERT | PROJECTION METHOD | CONVERGENCE | CQ-ALGORITHM | Information science | Management science | Business schools | Equality | Methods

Numeric Computing | Theory of Computation | Extended split equality problem | Weak convergence | Algorithms | Algebra | Numerical Analysis | Extended split equality fixed point problem | Computer Science | 47H09 | Simultaneous iterative algorithm | 47H05 | 47J25 | 47H06 | Fixed point | EIGENVALUE | MATHEMATICS, APPLIED | CONVEX FEASIBILITY | POLYNOMIAL OPTIMIZATION | HILBERT | PROJECTION METHOD | CONVERGENCE | CQ-ALGORITHM | Information science | Management science | Business schools | Equality | Methods

Journal Article

Numerical Algorithms, ISSN 1017-1398, 10/2018, Volume 79, Issue 2, pp. 529 - 553

Using the double projection and Halpern methods, we prove two strong convergence results for finding a solution of a variational inequality problem involving...

Quasi-nonexpansive mapping | Monotone mappings | Strong convergence | Numeric Computing | Hilbert spaces | Theory of Computation | Algorithms | Algebra | Numerical Analysis | Double projection Method | Computer Science | 47H09 | Halpern method | 47J05 | 47J25 | 47H06 | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | THEOREM | HYBRID METHOD | STEP | SUBGRADIENT EXTRAGRADIENT METHOD | BANACH-SPACES | GRADIENT-METHOD | STRONG-CONVERGENCE

Quasi-nonexpansive mapping | Monotone mappings | Strong convergence | Numeric Computing | Hilbert spaces | Theory of Computation | Algorithms | Algebra | Numerical Analysis | Double projection Method | Computer Science | 47H09 | Halpern method | 47J05 | 47J25 | 47H06 | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | THEOREM | HYBRID METHOD | STEP | SUBGRADIENT EXTRAGRADIENT METHOD | BANACH-SPACES | GRADIENT-METHOD | STRONG-CONVERGENCE

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 2/2019, Volume 180, Issue 2, pp. 451 - 479

In this paper, we adopt an iterative approach to solve the class of optimization problem for the sum of finite functions over split equality optimization...

65K15 | Mathematics | Theory of Computation | Optimization for the sum of finite functions | Optimization | Split equality quadratic signal recovery problem | 47H10 | 90C35 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | 47H09 | Split equality inconsistent feasibility problem | Split equality optimization problem | Applications of Mathematics | Engineering, general | 47J25 | 47H06 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FEASIBILITY PROBLEM | ALGORITHM | Problems | Theorems | Nonlinear analysis | Signal processing | Feasibility | Signal reconstruction | Linear equations | Equality | Convergence

65K15 | Mathematics | Theory of Computation | Optimization for the sum of finite functions | Optimization | Split equality quadratic signal recovery problem | 47H10 | 90C35 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | 47H09 | Split equality inconsistent feasibility problem | Split equality optimization problem | Applications of Mathematics | Engineering, general | 47J25 | 47H06 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FEASIBILITY PROBLEM | ALGORITHM | Problems | Theorems | Nonlinear analysis | Signal processing | Feasibility | Signal reconstruction | Linear equations | Equality | Convergence

Journal Article

Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 12/2019, Volume 21, Issue 4, pp. 1 - 21

We introduce two types of mappings, namely Reich type nonexpansive and Chatterjea type nonexpansive mappings, and derive some sufficient conditions under which...

Mathematical Methods in Physics | 47H10 | uniquely remotal set | Analysis | approximate fixed point sequence | M -compact | Mathematics, general | Mathematics | Nonexpansive map | 47H06 | MATHEMATICS | MATHEMATICS, APPLIED | M-compact | THEOREMS | FIXED-POINT PROPERTY | BANACH

Mathematical Methods in Physics | 47H10 | uniquely remotal set | Analysis | approximate fixed point sequence | M -compact | Mathematics, general | Mathematics | Nonexpansive map | 47H06 | MATHEMATICS | MATHEMATICS, APPLIED | M-compact | THEOREMS | FIXED-POINT PROPERTY | BANACH

Journal Article

Journal of Applied Analysis, ISSN 1425-6908, 12/2015, Volume 21, Issue 2, pp. 63 - 77

In this paper we propose an iterative algorithm based on the hybrid method in mathematical programming for approximating a common fixed point of an infinite...

equilibrium problem | 47H09 | reflexive Banach spaces | Legendre function | 47J05 | Bregman distance | 47J25 | resolvent | 47H06 | strong convergence

equilibrium problem | 47H09 | reflexive Banach spaces | Legendre function | 47J05 | Bregman distance | 47J25 | resolvent | 47H06 | strong convergence

Journal Article

Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 12/2017, Volume 19, Issue 4, pp. 3097 - 3118

Our interest in this paper is to prove a strong convergence result for finding a zero of the sum of two monotone operators, with one of the two operators being...

Haugazeau algorithm | Projection | Mathematics | Mathematical Methods in Physics | Analysis | 47H09 | Splitting algorithm | Mathematics, general | 47J05 | Strong Convergence | 47J25 | 47H06 | Nesterov method | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | GRADIENT PROJECTION METHOD | PROXIMAL POINT ALGORITHMS | ACCRETIVE-OPERATORS | VARIATIONAL-INEQUALITIES | MATHEMATICS | NONLINEAR OPERATORS | SPLITTING ALGORITHMS | CONVEX MINIMIZATION | BANACH-SPACE | Algorithms | Resveratrol

Haugazeau algorithm | Projection | Mathematics | Mathematical Methods in Physics | Analysis | 47H09 | Splitting algorithm | Mathematics, general | 47J05 | Strong Convergence | 47J25 | 47H06 | Nesterov method | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | GRADIENT PROJECTION METHOD | PROXIMAL POINT ALGORITHMS | ACCRETIVE-OPERATORS | VARIATIONAL-INEQUALITIES | MATHEMATICS | NONLINEAR OPERATORS | SPLITTING ALGORITHMS | CONVEX MINIMIZATION | BANACH-SPACE | Algorithms | Resveratrol

Journal Article

Acta Mathematica Vietnamica, ISSN 0251-4184, 3/2016, Volume 41, Issue 1, pp. 55 - 68

We consider a regularization method based on the Browder–Tikhonov and iterative regularization method that can be used to find a solution of a class of...

Variational inequality | Accretive mapping | 47H09 | Mathematics, general | Mathematics | 47J05 | 47J06 | Regularization | 47H06 | Nonexpansive mapping | Fixed point

Variational inequality | Accretive mapping | 47H09 | Mathematics, general | Mathematics | 47J05 | 47J06 | Regularization | 47H06 | Nonexpansive mapping | Fixed point

Journal Article

Journal of Evolution Equations, ISSN 1424-3199, 6/2018, Volume 18, Issue 2, pp. 1025 - 1047

We consider an anti-periodic evolution inclusion defined on an evolution triple of spaces, driven by an operator of monotone-type and with a multivalued...

34C25 | Strong relaxation | Analysis | Compact embedding | Convex and nonconvex problem | Evolution triple | Mathematics | Extremal trajectories | 47H06 | 34G25 | EXISTENCE | MATHEMATICS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | EQUATIONS | Computer science

34C25 | Strong relaxation | Analysis | Compact embedding | Convex and nonconvex problem | Evolution triple | Mathematics | Extremal trajectories | 47H06 | 34G25 | EXISTENCE | MATHEMATICS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | EQUATIONS | Computer science

Journal Article

Mathematische Annalen, ISSN 0025-5831, 5/2010, Volume 347, Issue 1, pp. 135 - 199

We prove existence and uniqueness of entropy solutions for the nonhomogeneous Dirichlet problem associated to the relativistic heat equation.

35K20 | Mathematics, general | Mathematics | 47H06 | 35K55 | 35K65 | MATHEMATICS | GROWTH FUNCTIONALS | QUASI-LINEAR EQUATION

35K20 | Mathematics, general | Mathematics | 47H06 | 35K55 | 35K65 | MATHEMATICS | GROWTH FUNCTIONALS | QUASI-LINEAR EQUATION

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. 2113 - 2126

Malitsky and Semenov in (Cybern Syst Anal 50(2):271–277, 2014) introduced a new extragradient method for variational inequality problem. This paper extends the...

Lipschitz-type continuous | Theoretical, Mathematical and Computational Physics | Mathematics | Subgradient extragradient method | Pseudomonotone bifunction | Equilibrium problem | Variational inequality | 47H09 | Mathematics, general | 47J05 | Applications of Mathematics | 47H05 | 47J25 | 47H06 | MATHEMATICS | ALGORITHM | FIXED-POINT | Algorithms | Iterative methods | Portfolio management | Optimization

Lipschitz-type continuous | Theoretical, Mathematical and Computational Physics | Mathematics | Subgradient extragradient method | Pseudomonotone bifunction | Equilibrium problem | Variational inequality | 47H09 | Mathematics, general | 47J05 | Applications of Mathematics | 47H05 | 47J25 | 47H06 | MATHEMATICS | ALGORITHM | FIXED-POINT | Algorithms | Iterative methods | Portfolio management | Optimization

Journal Article

Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 12/2017, Volume 19, Issue 4, pp. 2483 - 2510

In this paper, we present a proximal split feasibility algorithm with an additional inertial extrapolation term for solving a proximal split feasibility...

Mathematical Methods in Physics | Analysis | 47H09 | Mathematics, general | Mathematics | inertial term | 47J05 | Moreau–Yosida approximate | weak convergence | 47J25 | 47H06 | Proximal split feasibility problems | Moreau-Yosida approximate | HILBERT-SPACES | MATHEMATICS, APPLIED | CQ ALGORITHM | MATHEMATICS | THEOREMS | MONOTONE INCLUSION PROBLEMS | MAPPINGS | FORWARD-BACKWARD ALGORITHM | CONVEX MINIMIZATION | OPERATORS | POINT ALGORITHM | FIXED-POINTS | Methods | Algorithms

Mathematical Methods in Physics | Analysis | 47H09 | Mathematics, general | Mathematics | inertial term | 47J05 | Moreau–Yosida approximate | weak convergence | 47J25 | 47H06 | Proximal split feasibility problems | Moreau-Yosida approximate | HILBERT-SPACES | MATHEMATICS, APPLIED | CQ ALGORITHM | MATHEMATICS | THEOREMS | MONOTONE INCLUSION PROBLEMS | MAPPINGS | FORWARD-BACKWARD ALGORITHM | CONVEX MINIMIZATION | OPERATORS | POINT ALGORITHM | FIXED-POINTS | Methods | Algorithms

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2016, Volume 2016, Issue 1, pp. 1 - 28

Let E be a real normed space with dual space E ∗ $E^{*}$ and let A : E → 2 E ∗ $A:E\rightarrow2^{E^{*}}$ be any map. Let J : E → 2 E ∗...

monotone mapping | Mathematical and Computational Biology | Mathematics | Topology | strong convergence | J -pseudocontractive mapping | Analysis | Mathematics, general | Applications of Mathematics | Differential Geometry | 47H05 | 47J25 | 46N10 | 47H06 | 47H04 | J -fixed points | J-pseudocontractive mapping | J-fixed points | Algorithms | Approximation | Integral equations | Mathematical analysis | Texts | Complement | Mapping | Optimization

monotone mapping | Mathematical and Computational Biology | Mathematics | Topology | strong convergence | J -pseudocontractive mapping | Analysis | Mathematics, general | Applications of Mathematics | Differential Geometry | 47H05 | 47J25 | 46N10 | 47H06 | 47H04 | J -fixed points | J-pseudocontractive mapping | J-fixed points | Algorithms | Approximation | Integral equations | Mathematical analysis | Texts | Complement | Mapping | Optimization

Journal Article

Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 9/2017, Volume 19, Issue 3, pp. 2109 - 2128

The purpose of this paper is to introduce an iterative algorithm that does not require any knowledge of the operator norm for approximating a solution of a...

bounded linear operator | Mathematics | strong convergence | Mathematical Methods in Physics | fixed point | Analysis | 47H09 | Mathematics, general | Hilbert space | 47J05 | split generalised mixed equilibrium problem | 47J25 | kappa $$ κ -Pseudocontraction | 47H06 | κ-Pseudocontraction | STRICT PSEUDO-CONTRACTIONS | MATHEMATICS, APPLIED | STRONG-CONVERGENCE THEOREMS | VARIATIONAL-INEQUALITIES | MATHEMATICS | kappa-Pseudocontraction | APPROXIMATION METHOD | EXTRAGRADIENT METHOD | MAPPINGS | HYBRID ITERATIVE METHOD | Algorithms

bounded linear operator | Mathematics | strong convergence | Mathematical Methods in Physics | fixed point | Analysis | 47H09 | Mathematics, general | Hilbert space | 47J05 | split generalised mixed equilibrium problem | 47J25 | kappa $$ κ -Pseudocontraction | 47H06 | κ-Pseudocontraction | STRICT PSEUDO-CONTRACTIONS | MATHEMATICS, APPLIED | STRONG-CONVERGENCE THEOREMS | VARIATIONAL-INEQUALITIES | MATHEMATICS | kappa-Pseudocontraction | APPROXIMATION METHOD | EXTRAGRADIENT METHOD | MAPPINGS | HYBRID ITERATIVE METHOD | Algorithms

Journal Article