Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2012, Volume 385, Issue 1, pp. 458 - 465

We further develop a classical geometric construction of V. Klee and show, typically, that if X is a nonreflexive Banach space with separable dual, then X...

Fréchet differentiable norm | Locally uniformly rotund norm | Renormings | Rotund norm | Gâteaux differentiable norm | SPACE | MATHEMATICS | Gateaux differentiable norm | MATHEMATICS, APPLIED | Frechet differentiable norm | NORMS

Fréchet differentiable norm | Locally uniformly rotund norm | Renormings | Rotund norm | Gâteaux differentiable norm | SPACE | MATHEMATICS | Gateaux differentiable norm | MATHEMATICS, APPLIED | Frechet differentiable norm | NORMS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2006, Volume 318, Issue 1, pp. 288 - 295

Let K be a nonempty closed convex subset of a real Banach space E which has a uniformly Gâteaux differentiable norm and T:K→K be a nonexpansive mapping with...

Uniformly smooth real Banach spaces | Uniformly Gâteaux differentiable norm | MATHEMATICS | MATHEMATICS, APPLIED | uniformly Gateaux differentiable norm | uniformly smooth real Banach spaces | STRONG-CONVERGENCE

Uniformly smooth real Banach spaces | Uniformly Gâteaux differentiable norm | MATHEMATICS | MATHEMATICS, APPLIED | uniformly Gateaux differentiable norm | uniformly smooth real Banach spaces | STRONG-CONVERGENCE

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 17, pp. 6012 - 6023

In this paper we deal with fixed point computational problems by strongly convergent methods involving strictly pseudocontractive mappings in smooth Banach...

[formula omitted]-iteration process | [formula omitted]-strictly pseudocontractive | Metric projection mapping | Uniformly Gâteaux differentiable norm | Strongly pseudocontractive | Uniformly Gteaux differentiable norm | S-iteration process | λ-strictly pseudocontractive | FEASIBILITY PROBLEMS | HILBERT-SPACES | MATHEMATICS, APPLIED | APPROXIMATION | ACCRETIVE-OPERATORS | VARIATIONAL-INEQUALITIES | MATHEMATICS | Uniformly Gateaux differentiable norm | RESOLVENTS | THEOREMS | lambda-strictly pseudocontractive | WEAKLY CONTRACTIVE MAPS | PSEUDO-CONTRACTIONS | FIXED-POINTS | Theorems | Mathematical analysis | Steepest descent method | Inequalities | Nonlinearity | Mapping | Banach space | Convergence

[formula omitted]-iteration process | [formula omitted]-strictly pseudocontractive | Metric projection mapping | Uniformly Gâteaux differentiable norm | Strongly pseudocontractive | Uniformly Gteaux differentiable norm | S-iteration process | λ-strictly pseudocontractive | FEASIBILITY PROBLEMS | HILBERT-SPACES | MATHEMATICS, APPLIED | APPROXIMATION | ACCRETIVE-OPERATORS | VARIATIONAL-INEQUALITIES | MATHEMATICS | Uniformly Gateaux differentiable norm | RESOLVENTS | THEOREMS | lambda-strictly pseudocontractive | WEAKLY CONTRACTIVE MAPS | PSEUDO-CONTRACTIONS | FIXED-POINTS | Theorems | Mathematical analysis | Steepest descent method | Inequalities | Nonlinearity | Mapping | Banach space | Convergence

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 13, pp. 4293 - 4299

Let E be a 2 -uniformly real Banach space and F , K : E → E be nonlinear-bounded accretive operators. Assume that the Hammerstein equation u + K F u = 0 has a...

Accretive operators | Uniformly Gâteaux differentiable norm | Equations of Hammerstein type | Generalized duality maps | Modulus of smoothness | Uniformly Gteaux differentiable norm | EXISTENCE | MATHEMATICS | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | BANACH-SPACES | MONOTONE OPERATORS | Nonlinearity | Operators | Banach space | Integral equations | Mathematical analysis | Convergence

Accretive operators | Uniformly Gâteaux differentiable norm | Equations of Hammerstein type | Generalized duality maps | Modulus of smoothness | Uniformly Gteaux differentiable norm | EXISTENCE | MATHEMATICS | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | BANACH-SPACES | MONOTONE OPERATORS | Nonlinearity | Operators | Banach space | Integral equations | Mathematical analysis | Convergence

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2012, Volume 75, Issue 1, pp. 153 - 162

A new iterative method for approximating fixed points of bounded and continuous pseudocontractive mapping is proposed and a strong convergence theorem is...

Reflexive Banach spaces | Accretive mappings | Uniformly Gâteaux differentiable norm | Pseudocontractive operators | Uniformly Gteaux differentiable norm | MATHEMATICS | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | APPROXIMATION | MONOTONE | EQUATIONS | ACCRETIVE-OPERATORS | STRONG-CONVERGENCE THEOREMS | FIXED-POINTS | Operators | Theorems | Approximation | Nonlinearity | Mapping | Iterative methods | Convergence

Reflexive Banach spaces | Accretive mappings | Uniformly Gâteaux differentiable norm | Pseudocontractive operators | Uniformly Gteaux differentiable norm | MATHEMATICS | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | APPROXIMATION | MONOTONE | EQUATIONS | ACCRETIVE-OPERATORS | STRONG-CONVERGENCE THEOREMS | FIXED-POINTS | Operators | Theorems | Approximation | Nonlinearity | Mapping | Iterative methods | Convergence

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 01/2013, Volume 219, Issue 10, pp. 5657 - 5667

Let E be a q-uniformly smooth real Banach space. For each i=1,2,…m, let Fi,Ki:E→E be bounded and accretive mappings. Assume that the generalized Hammerstein...

Accretive operators | Duality maps | Uniformly Gâteaux differentiable norm | Equations of Hammerstein type | Modulus of smoothness | NONLINEAR INTEGRAL-EQUATIONS | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | INEQUALITIES | MONOTONE OPERATORS

Accretive operators | Duality maps | Uniformly Gâteaux differentiable norm | Equations of Hammerstein type | Modulus of smoothness | NONLINEAR INTEGRAL-EQUATIONS | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | INEQUALITIES | MONOTONE OPERATORS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2012, Volume 75, Issue 4, pp. 1859 - 1868

The main objectives of this paper are to employ a new proof technique to prove the strong convergence of { x n } and { y n } , defined respectively by x n + 1...

Uniformly Gâteaux differentiable norm | Accretive operator | Uniformly convex Banach space | Weakly continuous duality mapping | Uniformly Gteaux differentiable norm | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | ITERATIVE ALGORITHMS | MATHEMATICS | Uniformly Gateaux differentiable norm | NONLINEAR OPERATORS | MONOTONE | BANACH-SPACES | CONVERGENCE | ZEROS | Operators | Algorithms | Images | Norms | Nonlinearity | Mapping | Banach space | Convergence

Uniformly Gâteaux differentiable norm | Accretive operator | Uniformly convex Banach space | Weakly continuous duality mapping | Uniformly Gteaux differentiable norm | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | ITERATIVE ALGORITHMS | MATHEMATICS | Uniformly Gateaux differentiable norm | NONLINEAR OPERATORS | MONOTONE | BANACH-SPACES | CONVERGENCE | ZEROS | Operators | Algorithms | Images | Norms | Nonlinearity | Mapping | Banach space | Convergence

Journal Article

8.
Full Text
Strong convergence theorems for a common zero of a finite family of m -accretive mappings

Nonlinear Analysis, ISSN 0362-546X, 2007, Volume 66, Issue 5, pp. 1161 - 1169

Suppose K is a closed convex subset of a strictly convex real Banach space E which has a uniformly Gâteaux differentiable norm. Suppose that every nonempty...

Weakly compact sets | Accretive mappings | Uniformly Gâteaux differentiable norm | Pseudocontractive maps | Normalized duality maps | Strictly convex spaces | MATHEMATICS, APPLIED | normalized duality maps | EQUATIONS | ITERATIVE SOLUTION | pseudocontractive maps | MATHEMATICS | BANACH-SPACES | accretive mappings | strictly convex spaces | uniformly Gateaux differentiable norm | NONEXPANSIVE MAPPINGS | weakly compact sets | OPERATORS

Weakly compact sets | Accretive mappings | Uniformly Gâteaux differentiable norm | Pseudocontractive maps | Normalized duality maps | Strictly convex spaces | MATHEMATICS, APPLIED | normalized duality maps | EQUATIONS | ITERATIVE SOLUTION | pseudocontractive maps | MATHEMATICS | BANACH-SPACES | accretive mappings | strictly convex spaces | uniformly Gateaux differentiable norm | NONEXPANSIVE MAPPINGS | weakly compact sets | OPERATORS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2008, Volume 69, Issue 12, pp. 4732 - 4753

The purpose of this paper is to investigate the asymptotic behavior of algorithms for finding solutions for a certain class of variational inequalities V I D (...

Uniformly Gâteaux differentiable norm | Pseudocontractive mapping | Variational inequality | Weakly contraction | MATHEMATICS | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | RESOLVENTS | ACCRETIVE-OPERATORS | STRONG-CONVERGENCE THEOREMS | MONOTONE-OPERATORS | FIXED-POINTS | ZEROS | Analysis | Algorithms

Uniformly Gâteaux differentiable norm | Pseudocontractive mapping | Variational inequality | Weakly contraction | MATHEMATICS | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | RESOLVENTS | ACCRETIVE-OPERATORS | STRONG-CONVERGENCE THEOREMS | MONOTONE-OPERATORS | FIXED-POINTS | ZEROS | Analysis | Algorithms

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2008, Volume 69, Issue 10, pp. 3299 - 3309

Let X be a real strictly convex and reflexive Banach space with a uniformly Gâteaux differentiable norm and C be a nonempty closed convex subset of X . Let { T...

Strong convergence | Uniformly Gâteaux differentiable norm | Relaxed viscosity approximation method | Common fixed point | Nonexpansive mapping | MATHEMATICS | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | SEQUENCES | INFINITE NONEXPANSIVE-MAPPINGS | BANACH-SPACES | FINITE FAMILY | STRONG-CONVERGENCE | Analysis | Methods | Equality

Strong convergence | Uniformly Gâteaux differentiable norm | Relaxed viscosity approximation method | Common fixed point | Nonexpansive mapping | MATHEMATICS | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | SEQUENCES | INFINITE NONEXPANSIVE-MAPPINGS | BANACH-SPACES | FINITE FAMILY | STRONG-CONVERGENCE | Analysis | Methods | Equality

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 05/2014, Volume 233, pp. 369 - 376

In this paper, for Lipschitz accretive operator A, an iteration scheme is defined as follows:xn+1=(1-αn)xn+αn(u-βnAxn).Its strong convergence is established...

Accretive operator | Strong convergence | Uniformly Gâteaux differentiable norm | MATHEMATICS, APPLIED | EQUATIONS | PROXIMAL POINT ALGORITHM | STRONG-CONVERGENCE THEOREMS | Uniformly Gateaux differentiable norm | RESOLVENTS | MONOTONE | BANACH-SPACES | MAPPINGS | HILBERT-SPACE | FIXED POINTS

Accretive operator | Strong convergence | Uniformly Gâteaux differentiable norm | MATHEMATICS, APPLIED | EQUATIONS | PROXIMAL POINT ALGORITHM | STRONG-CONVERGENCE THEOREMS | Uniformly Gateaux differentiable norm | RESOLVENTS | MONOTONE | BANACH-SPACES | MAPPINGS | HILBERT-SPACE | FIXED POINTS

Journal Article

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Convergence theorems of iterative algorithms for continuous pseudocontractive mappings

Nonlinear Analysis, ISSN 0362-546X, 2007, Volume 67, Issue 2, pp. 486 - 497

In a real reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, we introduced the viscosity iterative process { x t }...

Strong convergence | Uniformly Gâteaux differentiable norm | Pseudocontractive mapping | Reflexive and strictly convex Banach space | Modified implicit iteration | modified implicit iteration | MATHEMATICS | MATHEMATICS, APPLIED | pseudocontractive mapping | uniformly Gateaux differentiable norm | strong convergence | reflexive and strictly convex Banach space | Algorithms

Strong convergence | Uniformly Gâteaux differentiable norm | Pseudocontractive mapping | Reflexive and strictly convex Banach space | Modified implicit iteration | modified implicit iteration | MATHEMATICS | MATHEMATICS, APPLIED | pseudocontractive mapping | uniformly Gateaux differentiable norm | strong convergence | reflexive and strictly convex Banach space | Algorithms

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2007, Volume 325, Issue 2, pp. 776 - 787

Let J ˜ be a commutative family of nonexpansive mappings of a closed convex subset C of a reflexive Banach space X such that the set of common fixed point is...

Strong convergence | Uniformly Gâteaux differentiable norm | Common fixed point | Viscosity approximation method | Nonexpansive mapping | APPROXIMATION METHODS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | nonexpansive mapping | ACCRETIVE-OPERATORS | STRONG-CONVERGENCE THEOREMS | strong convergence | MATHEMATICS | RESOLVENTS | uniformly gateaux differentiable norm | BANACH-SPACES | viscosity approximation method | common fixed point | FIXED-POINTS

Strong convergence | Uniformly Gâteaux differentiable norm | Common fixed point | Viscosity approximation method | Nonexpansive mapping | APPROXIMATION METHODS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | nonexpansive mapping | ACCRETIVE-OPERATORS | STRONG-CONVERGENCE THEOREMS | strong convergence | MATHEMATICS | RESOLVENTS | uniformly gateaux differentiable norm | BANACH-SPACES | viscosity approximation method | common fixed point | FIXED-POINTS

Journal Article

Journal of the Korean Mathematical Society, ISSN 0304-9914, 2017, Volume 54, Issue 3, pp. 1031 - 1047

In this paper, we introduce two general iterative algorithms (one implicit algorithm and other explicit algorithm) for nonexpansive mappings in a reflexive...

Strong positive linear operator | Fixed points | Uniformly Gâteaux differentiable norm | General iterative algorithms | Strongly pseudocontractive mapping | Nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | fixed points | strong positive linear operator | nonexpansive mapping | ACCRETIVE-OPERATORS | strongly pseudocontractive mapping | general iterative algorithms | uniformly Gateaux differentiable norm | FIXED-POINTS

Strong positive linear operator | Fixed points | Uniformly Gâteaux differentiable norm | General iterative algorithms | Strongly pseudocontractive mapping | Nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | fixed points | strong positive linear operator | nonexpansive mapping | ACCRETIVE-OPERATORS | strongly pseudocontractive mapping | general iterative algorithms | uniformly Gateaux differentiable norm | FIXED-POINTS

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...

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

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APPROXIMATION OF COMMON FIXED POINT OF FAMILIES OF NONLINEAR MAPPINGS WITH APPLICATIONS

数学物理学报：B辑英文版, ISSN 0252-9602, 2015, Volume 35, Issue 5, pp. 1225 - 1240

Abstract It is our purpose in this paper to show that some results obtained in uniformly convex real Banach space with uniformly Gateaux differentiable norm...

巴拿赫空间 | 映射族 | 非线性 | 平衡问题 | 一致Gateaux可微 | 伪压缩映象 | 不动点逼近 | 公共不动点 | nonexpansive mappings, reflexive real Banach spaces | uniformly Gâteaux differentiable norm | fixed point | 47H09 | 47J05 | 47J25 | 47H06 | Nonexpansive mappings, reflexive real Banach spaces | Uniformly Gâteaux differentiable norm | Fixed point | MATHEMATICS | SEMIGROUPS | NONEXPANSIVE-MAPPINGS | CONVERGENCE THEOREMS | reflexive real Banach spaces | COUNTABLE FAMILY | FINITE FAMILIES | uniformly Gateaux differentiable norm | nonexpansive mappings | ITERATION PROCESS | UNIFORMLY CONVEX

巴拿赫空间 | 映射族 | 非线性 | 平衡问题 | 一致Gateaux可微 | 伪压缩映象 | 不动点逼近 | 公共不动点 | nonexpansive mappings, reflexive real Banach spaces | uniformly Gâteaux differentiable norm | fixed point | 47H09 | 47J05 | 47J25 | 47H06 | Nonexpansive mappings, reflexive real Banach spaces | Uniformly Gâteaux differentiable norm | Fixed point | MATHEMATICS | SEMIGROUPS | NONEXPANSIVE-MAPPINGS | CONVERGENCE THEOREMS | reflexive real Banach spaces | COUNTABLE FAMILY | FINITE FAMILIES | uniformly Gateaux differentiable norm | nonexpansive mappings | ITERATION PROCESS | UNIFORMLY CONVEX

Journal Article

Taiwanese Journal of Mathematics, ISSN 1027-5487, 4/2015, Volume 19, Issue 2, pp. 481 - 503

It is known, by Rockafellar [ , 14 (1976), 877-898], that the proximal point algorithm (PPA) converges weakly to a zero of a maximal monotone operator in a...

Hilbert spaces | Mathematical monotonicity | Approximation | Banach space | Fixed point property | Regularization method | Strong convergence | Metric projection mapping | Maximal monotone operator | Resolvent identity | Uniformly Gâteaux differentiable norm | Proximal point algorithm | Accretive operator | VARIATIONAL-INEQUALITIES | MATHEMATICS | Uniformly Gateaux differentiable norm | MAPPINGS | POINT ALGORITHM | MONOTONE-OPERATORS

Hilbert spaces | Mathematical monotonicity | Approximation | Banach space | Fixed point property | Regularization method | Strong convergence | Metric projection mapping | Maximal monotone operator | Resolvent identity | Uniformly Gâteaux differentiable norm | Proximal point algorithm | Accretive operator | VARIATIONAL-INEQUALITIES | MATHEMATICS | Uniformly Gateaux differentiable norm | MAPPINGS | POINT ALGORITHM | MONOTONE-OPERATORS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2008, Volume 203, Issue 1, pp. 171 - 177

Let E be a uniformly convex Banach space with a uniformly Gâteaux differentiable norm, K a nonempty closed convex subset of E, T : K → K an asymptotically...

Uniformly Gâteaux differentiable norm | Asymptotically nonexpansive mapping | Variational inequality | Viscosity approximation | MATHEMATICS, APPLIED | variational inequality | asymptotically nonexpansive mapping | uniformly gateaux differentiable norm | viscosity approximation | THEOREMS

Uniformly Gâteaux differentiable norm | Asymptotically nonexpansive mapping | Variational inequality | Viscosity approximation | MATHEMATICS, APPLIED | variational inequality | asymptotically nonexpansive mapping | uniformly gateaux differentiable norm | viscosity approximation | THEOREMS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2009, Volume 212, Issue 1, pp. 51 - 59

By using viscosity approximation methods for asymptotically nonexpansive mappings in Banach spaces, some sufficient and necessary conditions for a new type of...

Asymptotically nonexpansive mappings | Uniformly Gâteaux differentiable norm | Normalized duality mapping | Viscosity approximation | Uniform normal structure | Fixed point | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | FIXED-POINTS | STRONG-CONVERGENCE

Asymptotically nonexpansive mappings | Uniformly Gâteaux differentiable norm | Normalized duality mapping | Viscosity approximation | Uniform normal structure | Fixed point | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | FIXED-POINTS | STRONG-CONVERGENCE

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2009, Volume 209, Issue 2, pp. 162 - 176

Let X be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. First purpose of this paper is to introduce a modified...

Strong convergence | Uniformly Gâteaux differentiable norm | Modified implicit iterative scheme with perturbed mapping | Pseudocontractive mapping | Reflexive and strictly convex Banach space | Modified viscosity iterative process with perturbed mapping | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | FINITE FAMILY | THEOREMS | ACCRETIVE-OPERATORS | Analysis | Algorithms

Strong convergence | Uniformly Gâteaux differentiable norm | Modified implicit iterative scheme with perturbed mapping | Pseudocontractive mapping | Reflexive and strictly convex Banach space | Modified viscosity iterative process with perturbed mapping | Uniformly Gateaux differentiable norm | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | FINITE FAMILY | THEOREMS | ACCRETIVE-OPERATORS | Analysis | Algorithms

Journal Article

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