Journal of Inequalities and Applications, ISSN 1025-5834, 12/2015, Volume 2015, Issue 1, pp. 1 - 11

In this paper, an iterative algorithm is introduced to solve the split common fixed point problem for asymptotically nonexpansive mappings in Hilbert spaces....

Analysis | Mathematics, general | split common fixed point problem | Mathematics | Hilbert space | Applications of Mathematics | asymptotically nonexpansive mapping | strong convergence | algorithm | MATHEMATICS | MATHEMATICS, APPLIED | FEASIBILITY PROBLEM | SETS | CQ ALGORITHM | Theorems | Fixed points (mathematics) | Asymptotic properties | Inequalities | Iterative algorithms | Mapping | Convergence

Analysis | Mathematics, general | split common fixed point problem | Mathematics | Hilbert space | Applications of Mathematics | asymptotically nonexpansive mapping | strong convergence | algorithm | MATHEMATICS | MATHEMATICS, APPLIED | FEASIBILITY PROBLEM | SETS | CQ ALGORITHM | Theorems | Fixed points (mathematics) | Asymptotic properties | Inequalities | Iterative algorithms | Mapping | Convergence

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2007, Volume 329, Issue 1, pp. 336 - 346

Let be a closed convex subset of a real Hilbert space and assume that is a -strict pseudo-contraction on with a fixed point, for some . Given an initial guess...

Mann's algorithm | Strict pseudo-contraction | Projection | Weak (strong) convergence | Fixed point | MATHEMATICS, APPLIED | APPROXIMATION | ACCRETIVE-OPERATORS | MODIFIED MANN ITERATIONS | ALGORITHMS | strict pseudo-contraction | MATHEMATICS | SEMIGROUPS | fixed point | BANACH-SPACES | weak (strong) convergence | EXAMPLE | projection | ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS | FIXED-POINTS | Algorithms

Mann's algorithm | Strict pseudo-contraction | Projection | Weak (strong) convergence | Fixed point | MATHEMATICS, APPLIED | APPROXIMATION | ACCRETIVE-OPERATORS | MODIFIED MANN ITERATIONS | ALGORITHMS | strict pseudo-contraction | MATHEMATICS | SEMIGROUPS | fixed point | BANACH-SPACES | weak (strong) convergence | EXAMPLE | projection | ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS | FIXED-POINTS | Algorithms

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2003, Volume 279, Issue 2, pp. 372 - 379

In this paper, we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in Hilbert spaces by the hybrid method in the...

Metric projection | Strong convergence | Resolvent | Nonexpansive | Nonexpansive semigroup | MATHEMATICS | MATHEMATICS, APPLIED | metric projection | APPROXIMATION | SPACES | nonexpansive semigroup | resolvent | strong convergence | MONOTONE-OPERATORS | FIXED-POINTS | nonexpansive

Metric projection | Strong convergence | Resolvent | Nonexpansive | Nonexpansive semigroup | MATHEMATICS | MATHEMATICS, APPLIED | metric projection | APPROXIMATION | SPACES | nonexpansive semigroup | resolvent | strong convergence | MONOTONE-OPERATORS | FIXED-POINTS | nonexpansive

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 225, Issue 1, pp. 20 - 30

The purpose of this paper is to introduce hybrid projection algorithms for finding a common element of the set of common fixed points of two quasi-...

Strong convergence | Equilibrium problem | Banach space | Quasi- [formula omitted]-nonexpansive mapping | Quasi-φ{symbol}-nonexpansive mapping | WEAK | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | ITERATIVE METHOD | Quasi-phi-nonexpansive mapping | Algorithms

Strong convergence | Equilibrium problem | Banach space | Quasi- [formula omitted]-nonexpansive mapping | Quasi-φ{symbol}-nonexpansive mapping | WEAK | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | ITERATIVE METHOD | Quasi-phi-nonexpansive mapping | Algorithms

Journal Article

5.
Full Text
Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem

Journal of Optimization Theory and Applications, ISSN 0022-3239, 6/2007, Volume 133, Issue 3, pp. 359 - 370

In this paper, we introduce two iterative sequences for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions...

Firmly nonexpansive mappings | Calculus of Variations and Optimal Control; Optimization | Equilibrium problems | Operations Research/Decision Theory | Weak and strong convergence | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Optimization | Nonexpansive mappings | Monotonicity | equilibrium problems | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | firmly nonexpansive mappings | weak and strong convergence | monotonicity | nonexpansive mappings | Studies | Mathematical models | Equilibrium | Convergence | Theorems | Hilbert space | Mapping

Firmly nonexpansive mappings | Calculus of Variations and Optimal Control; Optimization | Equilibrium problems | Operations Research/Decision Theory | Weak and strong convergence | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Optimization | Nonexpansive mappings | Monotonicity | equilibrium problems | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | firmly nonexpansive mappings | weak and strong convergence | monotonicity | nonexpansive mappings | Studies | Mathematical models | Equilibrium | Convergence | Theorems | Hilbert space | Mapping

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2010, Volume 216, Issue 12, pp. 3439 - 3449

In this paper, we introduce an iterative process which converges strongly to a common element of set of common fixed points of countably infinite family of...

Strongly monotone mappings | Monotone mappings | Strong convergence | Variational inequality problems | Equilibrium problem | [formula omitted]-inverse strongly monotone mappings | γ-inverse strongly monotone mappings | gamma-inverse strongly monotone mappings | WEAK | MATHEMATICS, APPLIED | BANACH-SPACES | OPERATORS | Theorems | Computation | Inequalities | Mapping | Mathematical models | Banach space | Iterative methods | Convergence

Strongly monotone mappings | Monotone mappings | Strong convergence | Variational inequality problems | Equilibrium problem | [formula omitted]-inverse strongly monotone mappings | γ-inverse strongly monotone mappings | gamma-inverse strongly monotone mappings | WEAK | MATHEMATICS, APPLIED | BANACH-SPACES | OPERATORS | Theorems | Computation | Inequalities | Mapping | Mathematical models | Banach space | Iterative methods | Convergence

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2005, Volume 61, Issue 3, pp. 341 - 350

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of...

Metric projection | Inverse-strongly monotone mapping | Strong convergence | Variational inequality | Nonexpansive mapping | MATHEMATICS, APPLIED | nonexpansive mapping | variational inequality | strong convergence | VARIATIONAL-INEQUALITIES | MATHEMATICS | inverse-strongly monotone mapping | metric projection | WEAK-CONVERGENCE | CONSTRUCTION | HILBERT-SPACE | OPERATORS | FIXED-POINTS

Metric projection | Inverse-strongly monotone mapping | Strong convergence | Variational inequality | Nonexpansive mapping | MATHEMATICS, APPLIED | nonexpansive mapping | variational inequality | strong convergence | VARIATIONAL-INEQUALITIES | MATHEMATICS | inverse-strongly monotone mapping | metric projection | WEAK-CONVERGENCE | CONSTRUCTION | HILBERT-SPACE | OPERATORS | FIXED-POINTS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 70, Issue 7, pp. 2707 - 2716

In this paper, we prove strong convergence theorems to a zero of monotone mapping and a fixed point of relatively weak nonexpansive mapping. Moreover, strong...

Strongly monotone mappings | variational inequality problems | Monotone mappings | Strong convergence | [formula omitted]-inverse strongly monotone mappings | Generalized projection | γ-inverse strongly monotone mappings | gamma-inverse strongly monotone mappings | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | BANACH-SPACES | OPERATORS

Strongly monotone mappings | variational inequality problems | Monotone mappings | Strong convergence | [formula omitted]-inverse strongly monotone mappings | Generalized projection | γ-inverse strongly monotone mappings | gamma-inverse strongly monotone mappings | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | BANACH-SPACES | OPERATORS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 217, Issue 19, pp. 7537 - 7545

The aim of this paper is to prove a strong convergence theorem for a pair of sequences of nonexpansive mappings in a Hilbert space, where one of them is a...

Strongly nonexpansive sequence | Strong convergence | Nonexpansive mapping | Fixed point | COMMON FIXED-POINTS | MATHEMATICS, APPLIED | BANACH-SPACES | MONOTONE MAPPINGS | OPERATORS | ITERATIVE SCHEMES | FAMILY | Theorems | Hilbert space | Mapping | Mathematical models | Computation | Convergence

Strongly nonexpansive sequence | Strong convergence | Nonexpansive mapping | Fixed point | COMMON FIXED-POINTS | MATHEMATICS, APPLIED | BANACH-SPACES | MONOTONE MAPPINGS | OPERATORS | ITERATIVE SCHEMES | FAMILY | Theorems | Hilbert space | Mapping | Mathematical models | Computation | Convergence

Journal Article

Journal of Computational Analysis and Applications, ISSN 1521-1398, 10/2020, Volume 28, Issue 5, pp. 903 - 916

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 5, pp. 1814 - 1822

Weak and strong convergence theorems are proved in real Hilbert spaces for a new class of nonspreading-type mappings more general than the class studied...

Weak convergence | Mean ergodic theorem | Strong convergence | Nonspreading mappings | Hilbert spaces | Fixed points | [formula omitted]-strictly pseudononspreading mappings | k-strictly pseudononspreading mappings | ITERATION | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | MATHEMATICS | NONLINEAR MAPPINGS | FIXED-POINT THEOREMS | BANACH-SPACES | OPERATORS | Nonlinearity | Theorems | Hilbert space | Mapping | Proving | Convergence

Weak convergence | Mean ergodic theorem | Strong convergence | Nonspreading mappings | Hilbert spaces | Fixed points | [formula omitted]-strictly pseudononspreading mappings | k-strictly pseudononspreading mappings | ITERATION | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | MATHEMATICS | NONLINEAR MAPPINGS | FIXED-POINT THEOREMS | BANACH-SPACES | OPERATORS | Nonlinearity | Theorems | Hilbert space | Mapping | Proving | Convergence

Journal Article

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

Weak and strong convergence theorems are proved in Hilbert spaces for new classes of multivalued demicontractive-type and hemicontractive-type mappings which...

Mathematical and Computational Biology | Analysis | hemicontractive-type mappings | Mathematics, general | Hilbert spaces | Mathematics | demicontractive-type mappings | weak and strong convergence | Applications of Mathematics | Topology | demiclosedness principle | Differential Geometry | Weak and strong convergence | Demiclosedness principle | Hemicontractive-type mappings | Demicontractive-type mappings | MATHEMATICS | ITERATION | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | HILBERT-SPACE | Fixed point theory | Usage | Convergence (Mathematics) | Hilbert space | Contraction operators | Theorems | Mapping | Convergence

Mathematical and Computational Biology | Analysis | hemicontractive-type mappings | Mathematics, general | Hilbert spaces | Mathematics | demicontractive-type mappings | weak and strong convergence | Applications of Mathematics | Topology | demiclosedness principle | Differential Geometry | Weak and strong convergence | Demiclosedness principle | Hemicontractive-type mappings | Demicontractive-type mappings | MATHEMATICS | ITERATION | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | HILBERT-SPACE | Fixed point theory | Usage | Convergence (Mathematics) | Hilbert space | Contraction operators | Theorems | Mapping | Convergence

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2007, Volume 67, Issue 5, pp. 1464 - 1473

Let be a uniformly convex Banach space which satisfies Opial’s condition or whose norm is Fréchet differentiable. Recently, Takahashi and Shimoji...

Iterative scheme | Strong convergence | Banach space | Common fixed point | Nonexpansive mapping | Sunny nonexpansive retraction | RETRACTIONS | MATHEMATICS, APPLIED | APPROXIMATION | SEQUENCES | nonexpansive mapping | iterative scheme | strong convergence | MATHEMATICS | NONLINEAR OPERATORS | SEMIGROUPS | FIXED-POINT THEOREMS | sunny nonexpansive retraction | CONVEX | BANACH-SPACES | common fixed point

Iterative scheme | Strong convergence | Banach space | Common fixed point | Nonexpansive mapping | Sunny nonexpansive retraction | RETRACTIONS | MATHEMATICS, APPLIED | APPROXIMATION | SEQUENCES | nonexpansive mapping | iterative scheme | strong convergence | MATHEMATICS | NONLINEAR OPERATORS | SEMIGROUPS | FIXED-POINT THEOREMS | sunny nonexpansive retraction | CONVEX | BANACH-SPACES | common fixed point

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2014, Volume 2014, Issue 1, pp. 1 - 11

In this paper, we propose an algorithms for finding a common fixed point of an infinite family of multi-valued generalized nonexpansive mappings in uniformly...

multi-valued mapping satisfying condition (C) | Mathematical and Computational Biology | Analysis | multi-valued generalized nonexpansive mapping | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | weak and strong convergence theorem | Multi-valued mapping satisfying condition (C) | Weak and strong convergence theorem | Multi-valued generalized nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | MANN | FIXED-POINT | Usage | Fixed point theory | Convergence (Mathematics) | Distributions, Theory of (Functional analysis) | Banach spaces | Contraction operators | Paper | Theorems | Mapping | Algorithms | Banach space | Convergence

multi-valued mapping satisfying condition (C) | Mathematical and Computational Biology | Analysis | multi-valued generalized nonexpansive mapping | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | weak and strong convergence theorem | Multi-valued mapping satisfying condition (C) | Weak and strong convergence theorem | Multi-valued generalized nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | MANN | FIXED-POINT | Usage | Fixed point theory | Convergence (Mathematics) | Distributions, Theory of (Functional analysis) | Banach spaces | Contraction operators | Paper | Theorems | Mapping | Algorithms | Banach space | Convergence

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2010, Volume 73, Issue 6, pp. 1562 - 1568

In this paper, we first obtain a weak mean convergence theorem of Baillon’s type for nonspreading mappings in a Hilbert space. Further, using an idea of mean...

Weak convergence | Mean ergodic theorem | Strong convergence | Nonspreading mapping | Fixed point | MATHEMATICS, APPLIED | APPROXIMATION | SEQUENCES | MATHEMATICS | COMMON FIXED-POINTS | BANACH-SPACES | ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS | OPERATORS | Nonlinearity | Theorems | Hilbert space | Mapping | Convergence

Weak convergence | Mean ergodic theorem | Strong convergence | Nonspreading mapping | Fixed point | MATHEMATICS, APPLIED | APPROXIMATION | SEQUENCES | MATHEMATICS | COMMON FIXED-POINTS | BANACH-SPACES | ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS | OPERATORS | Nonlinearity | Theorems | Hilbert space | Mapping | Convergence

Journal Article

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 01/2019, Volume 40, Issue 2, pp. 163 - 177

In this article, we introduce a faster iteration for finding a fixed point of G-monotone nonexpansive mapping in a uniformly convex Banach space with a...

G-convex interval | 47H10 | fixed point | directed graph | 47H09 | weak and strong convergence | G-monotone nonexpansive mapping | 54H25 | PARTIAL METRIC-SPACES | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | PARTIALLY ORDERED SETS | ITERATION PROCESS | CONTRACTIONS | Theorems | Fixed points (mathematics) | Mapping | Graph theory | Iterative methods | Banach space | Convergence

G-convex interval | 47H10 | fixed point | directed graph | 47H09 | weak and strong convergence | G-monotone nonexpansive mapping | 54H25 | PARTIAL METRIC-SPACES | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | PARTIALLY ORDERED SETS | ITERATION PROCESS | CONTRACTIONS | Theorems | Fixed points (mathematics) | Mapping | Graph theory | Iterative methods | Banach space | Convergence

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2008, Volume 55, Issue 11, pp. 2544 - 2553

In this paper, we prove some strong and weak convergence theorems using a modified iterative process for nonself asymptotically nonexpansive mappings in a...

Weak convergence | Nonself asymptotically nonexpansive mappings | Strong convergence | Modified iterative process | MATHEMATICS, APPLIED | BANACH-SPACES | WEAK-CONVERGENCE | modified iterative process | nonself asymptotically nonexpansive mappings | weak convergence | FIXED-POINT ITERATIONS | strong convergence | Theorems | Asymptotic properties | Mapping | Mathematical models | Banach space | Iterative methods | Convergence

Weak convergence | Nonself asymptotically nonexpansive mappings | Strong convergence | Modified iterative process | MATHEMATICS, APPLIED | BANACH-SPACES | WEAK-CONVERGENCE | modified iterative process | nonself asymptotically nonexpansive mappings | weak convergence | FIXED-POINT ITERATIONS | strong convergence | Theorems | Asymptotic properties | Mapping | Mathematical models | Banach space | Iterative methods | Convergence

Journal Article

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

In this paper, first, we introduce the condition (BP) which is weaker than the completely continuous mapping in Banach spaces. Second, we consider a simple...

uniformly convex Banach space | asymptotically nonexpansive nonself-mapping | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | strong convergence | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | FIXED-POINTS | Fixed point theory | Usage | Convergence (Mathematics) | Banach spaces | Theorems | Mapping | Banach space | Asymptotic properties | Convergence

uniformly convex Banach space | asymptotically nonexpansive nonself-mapping | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | strong convergence | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | FIXED-POINTS | Fixed point theory | Usage | Convergence (Mathematics) | Banach spaces | Theorems | Mapping | Banach space | Asymptotic properties | Convergence

Journal Article

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 12/2018, Volume 39, Issue 16, pp. 1806 - 1832

In this paper, motivated by Moreau's proximal algorithm, we give several algorithms and related weak and strong convergence theorems for minimization problems...

split feasible problem | 46B20 | 47H09 | Projection | 46N10 | strong convergence | proximal gradient algorithm | MATHEMATICS, APPLIED | FIXED-POINT | MAPPINGS | Theorems | Hilbert space | Algorithms | Optimization | Feasibility studies | Convergence

split feasible problem | 46B20 | 47H09 | Projection | 46N10 | strong convergence | proximal gradient algorithm | MATHEMATICS, APPLIED | FIXED-POINT | MAPPINGS | Theorems | Hilbert space | Algorithms | Optimization | Feasibility studies | Convergence

Journal Article

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, ISSN 0362-546X, 11/2008, Volume 69, Issue 9, pp. 3160 - 3173

In this paper, we discuss some properties of iterates generated by a strict pseudo-contraction or a finite family of strict pseudo-contractions in a real...

The Ishikawa-like iteration | MATHEMATICS, APPLIED | Strong convergence | NONEXPANSIVE-MAPPINGS | APPROXIMATION | ACCRETIVE-OPERATORS | Weak convergence | HILBERT SPACE | MATHEMATICS | NONLINEAR MAPPINGS | SEMIGROUPS | lambda-strict pseudo-contraction | The normal Mann iteration | 2-uniformly smooth Banach spaces | FIXED-POINTS

The Ishikawa-like iteration | MATHEMATICS, APPLIED | Strong convergence | NONEXPANSIVE-MAPPINGS | APPROXIMATION | ACCRETIVE-OPERATORS | Weak convergence | HILBERT SPACE | MATHEMATICS | NONLINEAR MAPPINGS | SEMIGROUPS | lambda-strict pseudo-contraction | The normal Mann iteration | 2-uniformly smooth Banach spaces | FIXED-POINTS

Journal Article

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