Mathematics, ISSN 2227-7390, 11/2018, Volume 6, Issue 11, p. 257

This paper uses the viscosity implicit midpoint rule to find common points of the fixed point set of a nonexpansive mapping and the zero point set of an accretive operator in Banach space...

Accretive operator | Viscosity implicit midpoint rule | Nonexpansive mapping | Zero point problem | MATHEMATICS | accretive operator | zero point problem | ERRORS | viscosity implicit midpoint rule | EXPANSIONS | EQUATIONS | nonexpansive mapping

Accretive operator | Viscosity implicit midpoint rule | Nonexpansive mapping | Zero point problem | MATHEMATICS | accretive operator | zero point problem | ERRORS | viscosity implicit midpoint rule | EXPANSIONS | EQUATIONS | nonexpansive mapping

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2013, Volume 2013, Issue 1, pp. 1 - 14

In this paper, common solutions of a family of nonexpansive mappings and an accretive operator are investigated based on a viscosity iterative method...

accretive operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | Applications of Mathematics | Topology | Differential Geometry | iterative scheme | strong convergence | Iterative scheme | Strong convergence | Accretive operator | Nonexpansive mapping | Fixed point | ITERATIVE PROCESS | APPROXIMATION | VARIATIONAL-INEQUALITIES | MATHEMATICS | SEMIGROUPS | HYBRID PROJECTION METHODS | EQUILIBRIUM PROBLEMS | FIXED-POINT PROBLEMS | Fixed point theory | Usage | Convergence (Mathematics) | Banach spaces | Contraction operators

accretive operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | Applications of Mathematics | Topology | Differential Geometry | iterative scheme | strong convergence | Iterative scheme | Strong convergence | Accretive operator | Nonexpansive mapping | Fixed point | ITERATIVE PROCESS | APPROXIMATION | VARIATIONAL-INEQUALITIES | MATHEMATICS | SEMIGROUPS | HYBRID PROJECTION METHODS | EQUILIBRIUM PROBLEMS | FIXED-POINT PROBLEMS | Fixed point theory | Usage | Convergence (Mathematics) | Banach spaces | Contraction operators

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2014, Volume 2014, Issue 1, pp. 1 - 18

The purpose of this paper is to prove some new theorems of strong convergence to common solutions for two finite families of accretive mappings in a real uniformly smooth and uniformly convex Banach...

common zeros | Mathematical and Computational Biology | Analysis | uniformly smooth (or convex) Banach space | Mathematics, general | Mathematics | Applications of Mathematics | Topology | accretive mapping | pseudo-contractive mapping | Differential Geometry | MATHEMATICS | NONLINEAR OPERATORS | ZERO | MATHEMATICS, APPLIED | APPROXIMATION | PROXIMAL POINT ALGORITHMS | STRONG-CONVERGENCE | Fixed point theory | Usage | Banach spaces | Iterative methods (Mathematics) | Contraction operators | Errors | Theorems | Mathematical analysis | Iterative algorithms | Mapping | Banach space | Convergence

common zeros | Mathematical and Computational Biology | Analysis | uniformly smooth (or convex) Banach space | Mathematics, general | Mathematics | Applications of Mathematics | Topology | accretive mapping | pseudo-contractive mapping | Differential Geometry | MATHEMATICS | NONLINEAR OPERATORS | ZERO | MATHEMATICS, APPLIED | APPROXIMATION | PROXIMAL POINT ALGORITHMS | STRONG-CONVERGENCE | Fixed point theory | Usage | Banach spaces | Iterative methods (Mathematics) | Contraction operators | Errors | Theorems | Mathematical analysis | Iterative algorithms | Mapping | Banach space | Convergence

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 9

... Access Hybrid method for a class of accretive variational inequalities involving nonexpansive mappings Yaqin Wang 1* and Hong-kun Xu 2 * Correspondence...

hybrid method | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | variational inequality | Applications of Mathematics | accretive mapping | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | Nonlinearity | Mapping | Banach space | Inequalities | Convergence

hybrid method | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | variational inequality | Applications of Mathematics | accretive mapping | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | Nonlinearity | Mapping | Banach space | Inequalities | Convergence

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 70, Issue 9, pp. 3110 - 3118

In this paper we propose a new modified Mann iteration for computing common fixed points of nonexpansive mappings in a Banach space...

Strong convergence | Accretive operator | Uniformly smooth | Nonexpansive mapping | Fixed point | MATHEMATICS | COMMON FIXED-POINTS | MATHEMATICS, APPLIED | SEQUENCES | BANACH-SPACES | VISCOSITY APPROXIMATION METHODS

Strong convergence | Accretive operator | Uniformly smooth | Nonexpansive mapping | Fixed point | MATHEMATICS | COMMON FIXED-POINTS | MATHEMATICS, APPLIED | SEQUENCES | BANACH-SPACES | VISCOSITY APPROXIMATION METHODS

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2015, Volume 2015, Issue 1, pp. 1 - 13

In this paper, we introduce a new viscosity approximation method by using the shrinking projection algorithm to approximate a common fixed point of a countable family of nonlinear mappings in a Banach space...

weak relatively nonexpansive mapping | 47H10 | fixed point | Analysis | viscosity approximation method | Mathematics, general | Mathematics | 37C25 | Applications of Mathematics | strong convergence | EXISTENCE | MATHEMATICS, APPLIED | ACCRETIVE-OPERATORS | FAMILY | VARIATIONAL-INEQUALITIES | MATHEMATICS | THEOREMS | CONVERGENCE | EQUILIBRIUM PROBLEMS | FIXED-POINT PROBLEMS | ZEROS | Viscosity | Operators | Algorithms | Approximation | Mathematical analysis | Inequalities | Mapping | Banach space | Convergence

weak relatively nonexpansive mapping | 47H10 | fixed point | Analysis | viscosity approximation method | Mathematics, general | Mathematics | 37C25 | Applications of Mathematics | strong convergence | EXISTENCE | MATHEMATICS, APPLIED | ACCRETIVE-OPERATORS | FAMILY | VARIATIONAL-INEQUALITIES | MATHEMATICS | THEOREMS | CONVERGENCE | EQUILIBRIUM PROBLEMS | FIXED-POINT PROBLEMS | ZEROS | Viscosity | Operators | Algorithms | Approximation | Mathematical analysis | Inequalities | Mapping | Banach space | Convergence

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 15

m-d-Accretive mappings, which are totally different from m-accretive mappings in non-Hilbertian Banach spaces, belong to another type of nonlinear mappings with practical backgrounds...

d -accretive mapping | common zeros | Lyapunov functional | retraction | Analysis | nonlinear elliptic equation | Mathematics, general | Mathematics | Applications of Mathematics | d-accretive mapping | MATHEMATICS | MATHEMATICS, APPLIED | Theorems | Approximation | Mathematical analysis | Inequalities | Nonlinearity | Mapping | Banach space | Convergence

d -accretive mapping | common zeros | Lyapunov functional | retraction | Analysis | nonlinear elliptic equation | Mathematics, general | Mathematics | Applications of Mathematics | d-accretive mapping | MATHEMATICS | MATHEMATICS, APPLIED | Theorems | Approximation | Mathematical analysis | Inequalities | Nonlinearity | Mapping | Banach space | Convergence

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2007, Volume 67, Issue 11, pp. 3058 - 3063

Let K be a nonempty closed convex subset of a Banach space E , T : K → K a continuous pseudo-contractive mapping. Suppose that { α n...

Continuous pseudo-contractive mappings | Strong and weak convergence | Mann type implicit iteration process | MATHEMATICS, APPLIED | STRICTLY PSEUDOCONTRACTIVE MAPPINGS | APPROXIMATION | continuous pseudo-contractive mappings | FINITE FAMILY | STRONGLY ACCRETIVE MAPPINGS | MATHEMATICS | CONVERGENCE THEOREMS | MAPS | ISHIKAWA | BANACH-SPACES | OPERATORS | strong and weak convergence | FIXED-POINTS

Continuous pseudo-contractive mappings | Strong and weak convergence | Mann type implicit iteration process | MATHEMATICS, APPLIED | STRICTLY PSEUDOCONTRACTIVE MAPPINGS | APPROXIMATION | continuous pseudo-contractive mappings | FINITE FAMILY | STRONGLY ACCRETIVE MAPPINGS | MATHEMATICS | CONVERGENCE THEOREMS | MAPS | ISHIKAWA | BANACH-SPACES | OPERATORS | strong and weak convergence | FIXED-POINTS

Journal Article

Abstract and applied analysis, ISSN 1085-3375, 6/2012, Volume 2012, pp. 1 - 11

We First introduce a three-step iterative algorithm for approximating the fixed points of the hemicontractive mappings in Banach spaces...

COMMON FIXED-POINTS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | CONVERGENCE THEOREMS | ERRORS | FINITE FAMILY | ACCRETIVE-OPERATORS | GENERAL VARIATIONAL-INEQUALITIES | PSEUDO-CONTRACTIVE MAPPINGS | LIPSCHITZ PSEUDOCONTRACTIONS | IMPLICIT | Studies | Hilbert space | Algorithms | Banach spaces | Iterative methods | Inequality | Iterative algorithms | Mapping | Approximation | Banach space | Convergence

COMMON FIXED-POINTS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | CONVERGENCE THEOREMS | ERRORS | FINITE FAMILY | ACCRETIVE-OPERATORS | GENERAL VARIATIONAL-INEQUALITIES | PSEUDO-CONTRACTIVE MAPPINGS | LIPSCHITZ PSEUDOCONTRACTIONS | IMPLICIT | Studies | Hilbert space | Algorithms | Banach spaces | Iterative methods | Inequality | Iterative algorithms | Mapping | Approximation | Banach space | Convergence

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2012, Volume 2012, Issue 1, pp. 1 - 9

In this work, we consider a general algorithm for a countable family of nonexpansive mappings in Banach spaces...

k -Lipschitzian | fixed points | Mathematical and Computational Biology | Mathematics | variational inequality | Topology | Banach space | strong convergence | η -strongly accretive | Analysis | Mathematics, general | Applications of Mathematics | Differential Geometry | Fixed points | Strong convergence | k-Lipschitzian | Variational inequality | η-strongly accretive | MATHEMATICS | eta-strongly accretive | MATHEMATICS, APPLIED | Fixed point theory | Usage | Convergence (Mathematics) | Banach spaces | Contraction operators | Mapping | Algorithms | Inequalities | Proving | Convergence

k -Lipschitzian | fixed points | Mathematical and Computational Biology | Mathematics | variational inequality | Topology | Banach space | strong convergence | η -strongly accretive | Analysis | Mathematics, general | Applications of Mathematics | Differential Geometry | Fixed points | Strong convergence | k-Lipschitzian | Variational inequality | η-strongly accretive | MATHEMATICS | eta-strongly accretive | MATHEMATICS, APPLIED | Fixed point theory | Usage | Convergence (Mathematics) | Banach spaces | Contraction operators | Mapping | Algorithms | Inequalities | Proving | Convergence

Journal Article

71.
Full Text
Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces

Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/1997, Volume 125, Issue 12, pp. 3641 - 3645

... \leq \alpha_n \leq 1 and T is a nonexpansive mapping from a closed convex subset of a Banach space into itself.

Mathematical theorems | Real numbers | Banach space | Perceptron convergence procedure | MATHEMATICS | MATHEMATICS, APPLIED | RESOLVENTS | THEOREMS | iteration | ACCRETIVE-OPERATORS | strong convergence | nonexpansive mappings | Banach limits

Mathematical theorems | Real numbers | Banach space | Perceptron convergence procedure | MATHEMATICS | MATHEMATICS, APPLIED | RESOLVENTS | THEOREMS | iteration | ACCRETIVE-OPERATORS | strong convergence | nonexpansive mappings | Banach limits

Journal Article

Mathematical Modelling and Analysis, ISSN 1392-6292, 01/2016, Volume 21, Issue 1, pp. 95 - 118

.... This algorithm is introduced for finding a common zero point for a countable family of inverse strongly accretive operators and a countable family of nonexpansive mappings in Banach spaces...

inverse strongly accretive operator | nonexpansive mapping | Proximal Point Algorithm | Zero point | MATHEMATICS | ERRORS | NONLINEAR EQUATIONS | VISCOSITY APPROXIMATION METHODS | ITERATIVE PROCESSES | FIXED-POINTS | Operators (mathematics) | Algorithms | Approximation | Mathematical models | Inverse | Mapping | Banach space | Convergence

inverse strongly accretive operator | nonexpansive mapping | Proximal Point Algorithm | Zero point | MATHEMATICS | ERRORS | NONLINEAR EQUATIONS | VISCOSITY APPROXIMATION METHODS | ITERATIVE PROCESSES | FIXED-POINTS | Operators (mathematics) | Algorithms | Approximation | Mathematical models | Inverse | Mapping | Banach space | Convergence

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2013, Volume 2013, Issue 1, pp. 1 - 16

In this paper, we first introduce a new Halpern-type iterative scheme to approximate common fixed points of an infinite family of quasi-nonexpansive mappings and obtain a strongly convergent iterative...

accretive operator | sunny nonexpansive retraction | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | strong convergence | Strong convergence | Accretive operator | Fixed point | Sunny nonexpansive retraction | MATHEMATICS | MATHEMATICS, APPLIED | Fixed point theory | Usage | Banach spaces | Contraction operators

accretive operator | sunny nonexpansive retraction | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | strong convergence | Strong convergence | Accretive operator | Fixed point | Sunny nonexpansive retraction | MATHEMATICS | MATHEMATICS, APPLIED | Fixed point theory | Usage | Banach spaces | Contraction operators

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 8

We study the convergence of a more general Picard iterative sequence for nonexpansive and Lipschitz strongly accretive mappings in an arbitrary real Banach space...

Lipschitz mapping | Picard iteration | strongly accretive mapping | Analysis | Mathematics, general | Mathematics | strongly pseudocontractive mapping | Applications of Mathematics | Banach space | nonexpansive mappings | Strongly pseudocontractive mapping | Nonexpansive mappings | Strongly accretive mapping | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | NONLINEAR LIPSCHITZIAN | FIXED-POINTS

Lipschitz mapping | Picard iteration | strongly accretive mapping | Analysis | Mathematics, general | Mathematics | strongly pseudocontractive mapping | Applications of Mathematics | Banach space | nonexpansive mappings | Strongly pseudocontractive mapping | Nonexpansive mappings | Strongly accretive mapping | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | NONLINEAR LIPSCHITZIAN | FIXED-POINTS

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2008, Volume 2008, Issue 1, pp. 1 - 9

The purpose of this paper is to consider that a modified Halpern's iterative sequence converges strongly to a fixed point of nonexpansive mappings in Banach spaces which have a...

Mathematical and Computational Biology | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | MATHEMATICS | RESOLVENTS | APPROXIMATION | BANACH-SPACES | THEOREMS | ACCRETIVE-OPERATORS | FIXED-POINTS | Studies | Banach spaces

Mathematical and Computational Biology | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | MATHEMATICS | RESOLVENTS | APPROXIMATION | BANACH-SPACES | THEOREMS | ACCRETIVE-OPERATORS | FIXED-POINTS | Studies | Banach spaces

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 10

...) for a k-strictly pseudocontractive mapping, where satisfies the conditions: (C1) and (C2) , respectively. The results presented in this work improve the corresponding ones announced by many other authors.

Mathematics, general | Mathematics | Applications of Mathematics | Analysis | MATHEMATICS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | RESOLVENTS | APPROXIMATION | BANACH-SPACES | THEOREMS | ACCRETIVE-OPERATORS | FIXED-POINTS

Mathematics, general | Mathematics | Applications of Mathematics | Analysis | MATHEMATICS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | RESOLVENTS | APPROXIMATION | BANACH-SPACES | THEOREMS | ACCRETIVE-OPERATORS | FIXED-POINTS

Journal Article

Optimization: International Workshop on Nonlinear and Variational Analysis 2017, ISSN 0233-1934, 09/2018, Volume 67, Issue 9, pp. 1377 - 1388

In this paper, a new iterative method for finding the projection onto the intersection of two closed convex sets in the framework of Banach spaces is...

variational inequality | projection | Accretive operator | resolvent | strong convergence | 47J20 | 90C33 | 47H09 | 47N10 | 47H06 | WEAK | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPERATORS | FIXED-POINTS | Computational geometry | Iterative algorithms | Convexity | Banach space | Convergence

variational inequality | projection | Accretive operator | resolvent | strong convergence | 47J20 | 90C33 | 47H09 | 47N10 | 47H06 | WEAK | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPERATORS | FIXED-POINTS | Computational geometry | Iterative algorithms | Convexity | Banach space | Convergence

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2011, Volume 2011, Issue 1, pp. 1 - 10

We study the strong convergence of a regularization proximal point algorithm for finding a common fixed point of a finite family of nonexpansive mappings in a uniformly convex and uniformly smooth Banach space...

uniformly smooth and uniformly convex | mapping | weak sequential continuous | Mathematical and Computational Biology | regularization | Mathematics | Topology | Banach space | sunny nonexpansive retraction | accretive operators | Analysis | Mathematics, general | Applications of Mathematics | Differential Geometry | Accretive operators | Uniformly smooth and uniformly convex | Weak sequential continuous | Mapping | Regularization | Sunny nonexpansive retraction | MATHEMATICS | STRONG-CONVERGENCE THEOREMS | Usage | Fixed point theory | Transformations (Mathematics) | Banach spaces | Point mappings (Mathematics) | Methods | Fixed points (mathematics) | Algorithms | Mathematical analysis | Classification | Convergence

uniformly smooth and uniformly convex | mapping | weak sequential continuous | Mathematical and Computational Biology | regularization | Mathematics | Topology | Banach space | sunny nonexpansive retraction | accretive operators | Analysis | Mathematics, general | Applications of Mathematics | Differential Geometry | Accretive operators | Uniformly smooth and uniformly convex | Weak sequential continuous | Mapping | Regularization | Sunny nonexpansive retraction | MATHEMATICS | STRONG-CONVERGENCE THEOREMS | Usage | Fixed point theory | Transformations (Mathematics) | Banach spaces | Point mappings (Mathematics) | Methods | Fixed points (mathematics) | Algorithms | Mathematical analysis | Classification | Convergence

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2006, Volume 324, Issue 2, pp. 1105 - 1114

We introduce a new class of uniformly R-subweakly commuting mappings and then using this class study the problem of approximation of common fixed points of asymptotically S-nonexpansive mappings...

Strong convergence | Banach space | Uniformly R-subweakly commuting mappings | Asymptotically S-nonexpansive mappings | Gâteaux differentiable norm | Gateaux differentiable norm | MATHEMATICS, APPLIED | ACCRETIVE-OPERATORS | asymptotically S-nonexpansive mappings | STRONG-CONVERGENCE THEOREMS | strong convergence | WEAK | MATHEMATICS | MAPS | BANACH-SPACES | uniformly R-subweakly commuting mappings | ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS | Engineering schools | Management science

Strong convergence | Banach space | Uniformly R-subweakly commuting mappings | Asymptotically S-nonexpansive mappings | Gâteaux differentiable norm | Gateaux differentiable norm | MATHEMATICS, APPLIED | ACCRETIVE-OPERATORS | asymptotically S-nonexpansive mappings | STRONG-CONVERGENCE THEOREMS | strong convergence | WEAK | MATHEMATICS | MAPS | BANACH-SPACES | uniformly R-subweakly commuting mappings | ASYMPTOTICALLY NONEXPANSIVE-MAPPINGS | Engineering schools | Management science

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 2/2012, Volume 152, Issue 2, pp. 351 - 365

We study the strong convergence of a regularization proximal point algorithm for the problem of finding a common fixed point of a finite family of nonexpansive mappings in a uniformly convex...

Uniformly smooth and uniformly convex Banach space | Accretive operators | Weak sequential continuous mapping | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Regularization | Optimization | Sunny nonexpansive retraction | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION | STRONG-CONVERGENCE THEOREMS | Algorithms | Studies | Mapping | Banach spaces | Fixed points (mathematics) | Mathematical analysis | Banach space | Convergence

Uniformly smooth and uniformly convex Banach space | Accretive operators | Weak sequential continuous mapping | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Regularization | Optimization | Sunny nonexpansive retraction | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION | STRONG-CONVERGENCE THEOREMS | Algorithms | Studies | Mapping | Banach spaces | Fixed points (mathematics) | Mathematical analysis | Banach space | Convergence

Journal Article

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