Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2019, Volume 478, Issue 2, pp. 790 - 805

We study a convergence criterion which generalises the notion of being monotonically decreasing, and introduce a quantitative version of this criterion, a so...

Fixed points | Asymptotically nonexpansive mappings | Uniformly convex Banach spaces | Proof mining | Metastability | MATHEMATICS | MATHEMATICS, APPLIED

Fixed points | Asymptotically nonexpansive mappings | Uniformly convex Banach spaces | Proof mining | Metastability | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 2018, Volume 99, Issue 2, pp. 1 - 9

In 1965, Browder proved the existence of a common fixed point for commuting families of nonexpansive mappings acting on nonempty bounded closed convex subsets...

2010 Mathematics subject classification | 47H10 | secondary 47H09 | primary 47H20 | MATHEMATICS | asymptotic centre | common fixed point | nonexpansive mapping | amenability | uniformly convex space

2010 Mathematics subject classification | 47H10 | secondary 47H09 | primary 47H20 | MATHEMATICS | asymptotic centre | common fixed point | nonexpansive mapping | amenability | uniformly convex space

Journal Article

Commentarii Mathematici Helvetici, ISSN 0010-2571, 2016, Volume 91, Issue 2, pp. 203 - 218

We show that for acylindrically hyperbolic groups $\Gamma$ (with no nontrivial finite normal subgroups) and arbitrary unitary representation $\rho$ of $\Gamma$...

Group theory and generalizations | Functional analysis | Acylindrically hyperbolic groups | Uniformly convex Banach space | Second bounded cohomology

Group theory and generalizations | Functional analysis | Acylindrically hyperbolic groups | Uniformly convex Banach space | Second bounded cohomology

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 15

In this paper, our aim is to ascertain the distance between two sets iteratively in two simultaneous ways with the help of a multivalued coupling define for...

47H10 | Analysis | Optimal approximate solution | Mathematics, general | Best proximity pair | Mathematics | Metric spaces | Applications of Mathematics | 54H10 | Coupling | Uniformly convex Banach space | 54H25 | EXISTENCE | CYCLIC CONTRACTIVE MAPS | MATHEMATICS, APPLIED | MATHEMATICS | FIXED-POINT THEOREMS | MAPPINGS | PROXIMITY POINTS | ORDERED METRIC-SPACES | Couplings | Error analysis | Banach spaces | Banach space | Research

47H10 | Analysis | Optimal approximate solution | Mathematics, general | Best proximity pair | Mathematics | Metric spaces | Applications of Mathematics | 54H10 | Coupling | Uniformly convex Banach space | 54H25 | EXISTENCE | CYCLIC CONTRACTIVE MAPS | MATHEMATICS, APPLIED | MATHEMATICS | FIXED-POINT THEOREMS | MAPPINGS | PROXIMITY POINTS | ORDERED METRIC-SPACES | Couplings | Error analysis | Banach spaces | Banach space | Research

Journal Article

数学年刊：B辑英文版, ISSN 0252-9599, 2014, Volume 35, Issue 5, pp. 733 - 742

In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding into Banach...

一致凸空间 | 嵌入 | 度量空间 | 一致凸Banach空间 | 证明 | 子群 | Coarse embedding | Uniformly convex Banach spaces | 46B20 | 51F99 | Mathematics, general | Mathematics | Applications of Mathematics | Relative hyperbolic groups | MATHEMATICS | EMBEDDABILITY | BAUM-CONNES CONJECTURE | HILBERT-SPACE | RELATIVELY HYPERBOLIC GROUPS | Computer science

一致凸空间 | 嵌入 | 度量空间 | 一致凸Banach空间 | 证明 | 子群 | Coarse embedding | Uniformly convex Banach spaces | 46B20 | 51F99 | Mathematics, general | Mathematics | Applications of Mathematics | Relative hyperbolic groups | MATHEMATICS | EMBEDDABILITY | BAUM-CONNES CONJECTURE | HILBERT-SPACE | RELATIVELY HYPERBOLIC GROUPS | Computer science

Journal Article

Journal of Convex Analysis, ISSN 0944-6532, 2018, Volume 25, Issue 4, pp. 1291 - 1318

It is well known in convex analysis that proximal mappings on Hilbert spaces are 1-Lipschitz. In the present paper we show that proximal mappings on uniformly...

Modulus of uniform convexity | Proximal mapping | Convex function | Young function | Duality mapping | Uniformly convex function | Uniformly convex Banach space | uniformly convex Banach space | INEQUALITIES | APPROXIMATION | modulus of uniform convexity | uniformly convex function | SMOOTHNESS | duality mapping | MATHEMATICS | ENVELOPES | proximal mapping | SETS | ANALYSE FONCTIONNELLE | CONVERGENCE | REGULARIZATION | OPERATORS

Modulus of uniform convexity | Proximal mapping | Convex function | Young function | Duality mapping | Uniformly convex function | Uniformly convex Banach space | uniformly convex Banach space | INEQUALITIES | APPROXIMATION | modulus of uniform convexity | uniformly convex function | SMOOTHNESS | duality mapping | MATHEMATICS | ENVELOPES | proximal mapping | SETS | ANALYSE FONCTIONNELLE | CONVERGENCE | REGULARIZATION | OPERATORS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2011, Volume 363, Issue 4, pp. 2211 - 2247

We continue the study of prox-regular sets that we began in a previous work in the setting of uniformly convex Banach spaces endowed with a norm both uniformly...

Tangents | Real numbers | Serenity | Mathematical functions | Convexity | Indicator functions | Banach space | Normal vectors | Distance functions | Variational analysis | Distance function | Prox-regular set | Epigraph | Metric projection mapping | Proximal normal | Uniformly convex Banach space | uniformly convex Banach space | HILBERT-SPACES | metric projection mapping | INEQUALITIES | DIFFERENTIABILITY | variational analysis | proximal normal | METRIC REGULARITY | prox-regular set | LOWER NICE FUNCTIONS | epigraph | MATHEMATICS | CLOSED-SETS | BOUNDARIES | INTEGRATION | NONCONVEX SWEEPING PROCESS | SUBDIFFERENTIALS

Tangents | Real numbers | Serenity | Mathematical functions | Convexity | Indicator functions | Banach space | Normal vectors | Distance functions | Variational analysis | Distance function | Prox-regular set | Epigraph | Metric projection mapping | Proximal normal | Uniformly convex Banach space | uniformly convex Banach space | HILBERT-SPACES | metric projection mapping | INEQUALITIES | DIFFERENTIABILITY | variational analysis | proximal normal | METRIC REGULARITY | prox-regular set | LOWER NICE FUNCTIONS | epigraph | MATHEMATICS | CLOSED-SETS | BOUNDARIES | INTEGRATION | NONCONVEX SWEEPING PROCESS | SUBDIFFERENTIALS

Journal Article

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 03/2017, Volume 38, Issue 3, pp. 360 - 375

In this article, we prove that every nonempty and convex pair of subsets of uniformly convex in every direction Banach spaces has the proximal normal structure...

cyclic relatively nonexpansive mapping | uniformly convex Banach space | 47H10 | proximal normal structure | 47H09 | 46B20 | Best proximity point | EXISTENCE | MATHEMATICS, APPLIED | METRIC-SPACES | THEOREM | CONVERGENCE | PROXIMITY POINTS | MEIR-KEELER CONTRACTIONS | RELATIVELY NONEXPANSIVE-MAPPINGS | Proximity | Error analysis | Banach spaces | Theorems | Mapping | Functional analysis | Banach space | Optimization

cyclic relatively nonexpansive mapping | uniformly convex Banach space | 47H10 | proximal normal structure | 47H09 | 46B20 | Best proximity point | EXISTENCE | MATHEMATICS, APPLIED | METRIC-SPACES | THEOREM | CONVERGENCE | PROXIMITY POINTS | MEIR-KEELER CONTRACTIONS | RELATIVELY NONEXPANSIVE-MAPPINGS | Proximity | Error analysis | Banach spaces | Theorems | Mapping | Functional analysis | Banach space | Optimization

Journal Article

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

In this paper, we prove strong and weak convergence theorems for a mapping defined on a bounded, closed and convex subset of a uniformly convex Banach space,...

uniformly convex Banach space | fixed points | Mathematical and Computational Biology | generalized nonexpansive mappings | Mathematics | Topology | convergence theorem | 47H10 | Analysis | 47H09 | Mathematics, general | Applications of Mathematics | Differential Geometry | MATHEMATICS | FIXED-POINT THEOREMS | WEAK-CONVERGENCE | Usage | Convergence (Mathematics) | Banach spaces | Mappings (Mathematics) | Theorems | Paper | Nonlinearity | Mapping | Banach space | Dynamical systems | Convergence

uniformly convex Banach space | fixed points | Mathematical and Computational Biology | generalized nonexpansive mappings | Mathematics | Topology | convergence theorem | 47H10 | Analysis | 47H09 | Mathematics, general | Applications of Mathematics | Differential Geometry | MATHEMATICS | FIXED-POINT THEOREMS | WEAK-CONVERGENCE | Usage | Convergence (Mathematics) | Banach spaces | Mappings (Mathematics) | Theorems | Paper | Nonlinearity | Mapping | Banach space | Dynamical systems | Convergence

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 02/2017, Volume 95, Issue 1, pp. 149 - 156

In this paper we first give a negative answer to a question of Amini-Harandi ['Best proximity point theorems for cyclic strongly quasi-contraction mappings',...

uniformly convex Banach space | cyclic quasi-contraction | best proximity point | MATHEMATICS | MAPPINGS

uniformly convex Banach space | cyclic quasi-contraction | best proximity point | MATHEMATICS | MAPPINGS

Journal Article

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

This paper aims to study the strong convergence of generalized modified Krasnoselskii iterative process for finding the minimum norm solutions of certain...

uniformly convex Banach spaces | Mathematical and Computational Biology | Mathematics | Topology | minimum norm solutions | 47H10 | Analysis | Mathematics, general | generalized modified Krasnoselskii iterative | generalized strictly pseudocontractive mappings | Applications of Mathematics | Differential Geometry | 47H05 | Nonlinear equations | Mathematical analysis | Coercive force | Norms | Nonlinearity | Mapping | Banach space | Convergence

uniformly convex Banach spaces | Mathematical and Computational Biology | Mathematics | Topology | minimum norm solutions | 47H10 | Analysis | Mathematics, general | generalized modified Krasnoselskii iterative | generalized strictly pseudocontractive mappings | Applications of Mathematics | Differential Geometry | 47H05 | Nonlinear equations | Mathematical analysis | Coercive force | Norms | Nonlinearity | Mapping | Banach space | Convergence

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 5, pp. 1694 - 1701

The purpose of this paper is to prove the existence of a fixed point for a pointwise eventually nonexpansive mapping in a nearly uniformly convex Banach space....

Nearly uniformly convex Banach space | Edelstein’s method | Pointwise eventually nonexpansive mapping | Fixed point | Edelstein's method | MATHEMATICS | MATHEMATICS, APPLIED | CONTRACTIONS | Nonlinearity | Theorems | Mapping | Banach space | Asymptotic properties | Fixed points (mathematics)

Nearly uniformly convex Banach space | Edelstein’s method | Pointwise eventually nonexpansive mapping | Fixed point | Edelstein's method | MATHEMATICS | MATHEMATICS, APPLIED | CONTRACTIONS | Nonlinearity | Theorems | Mapping | Banach space | Asymptotic properties | Fixed points (mathematics)

Journal Article

STUDIA MATHEMATICA, ISSN 0039-3223, 2018, Volume 241, Issue 3, pp. 241 - 256

It is shown that there exists a non-separable uniformly convex Banach space on which every bounded linear operator is the sum of a scalar multiple of the...

uniformly convex | MATHEMATICS | DECOMPOSITIONS | separable range | few operators | SEQUENCE | COMPACT-OPERATORS | C(K) | WEAK HILBERT-SPACE

uniformly convex | MATHEMATICS | DECOMPOSITIONS | separable range | few operators | SEQUENCE | COMPACT-OPERATORS | C(K) | WEAK HILBERT-SPACE

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2012, Volume 2012, Issue 1, pp. 1 - 7

We introduce a condition on mappings, namely condition . In a uniformly convex Banach space, the condition is weaker than quasi-nonexpansiveness and weaker...

uniformly convex Banach space | Mathematical and Computational Biology | Analysis | common fixed point | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | quasi-nonexpansive mapping | generalized nonexpansive mapping | Quasi-nonexpansive mapping | Common fixed point | Uniformly convex Banach space | Generalized nonexpansive mapping | Fixed point theory | Hilbert space | Research | Mappings (Mathematics) | Fixed points (mathematics) | Mapping | Banach space | Existence theorems | Asymptotic properties

uniformly convex Banach space | Mathematical and Computational Biology | Analysis | common fixed point | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | quasi-nonexpansive mapping | generalized nonexpansive mapping | Quasi-nonexpansive mapping | Common fixed point | Uniformly convex Banach space | Generalized nonexpansive mapping | Fixed point theory | Hilbert space | Research | Mappings (Mathematics) | Fixed points (mathematics) | Mapping | Banach space | Existence theorems | Asymptotic properties

Journal Article

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, ISSN 1735-8515, 06/2017, Volume 43, Issue 3, pp. 617 - 627

In this paper, we prove some theorems related to properties of generalized symmetric hybrid mappings in Banach spaces. Using Banach limits, we prove a fixed...

MATHEMATICS | uniformly convex Banach space | HILBERT-SPACES | NONLINEAR MAPPINGS | FIXED-POINT THEOREMS | NONEXPANSIVE-MAPPINGS | hybrid method | ITERATION METHOD | Opial's condition | EXAMPLE | weak convergence | Fixed point

MATHEMATICS | uniformly convex Banach space | HILBERT-SPACES | NONLINEAR MAPPINGS | FIXED-POINT THEOREMS | NONEXPANSIVE-MAPPINGS | hybrid method | ITERATION METHOD | Opial's condition | EXAMPLE | weak convergence | Fixed point

Journal Article

Quaestiones Mathematicae, ISSN 1607-3606, 03/2016, Volume 39, Issue 2, pp. 203 - 215

A new class of noncyclic mappings, called generalized noncyclic relatively nonexpansive, is introduced and used to study the existence of best proximity pairs...

generalized noncyclic relatively nonexpansive | 47H09 | 46B20 | uniformly convex Banach space | Best proximity pair | 47H10 | EXISTENCE | MATHEMATICS | POINTS | RELATIVELY NONEXPANSIVE-MAPPINGS | Error analysis | Banach spaces

generalized noncyclic relatively nonexpansive | 47H09 | 46B20 | uniformly convex Banach space | Best proximity pair | 47H10 | EXISTENCE | MATHEMATICS | POINTS | RELATIVELY NONEXPANSIVE-MAPPINGS | Error analysis | Banach spaces

Journal Article

Israel Journal of Mathematics, ISSN 0021-2172, 6/2014, Volume 200, Issue 1, pp. 419 - 422

We use a self-improvement argument to give a very short and elementary proof of the result of Bourgain saying that infinite regular trees do not admit...

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | Functional Analysis | Metric Geometry

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | Functional Analysis | Metric Geometry

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 5

This paper is concerned with a new method to prove the weak convergence of a strictly pseudo-contractive mapping in a p-uniformly convex Banach space with more...

uniformly convex Banach space | Analysis | Mathematics, general | nonexpansive mapping | Mann iteration | Mathematics | Applications of Mathematics | strictly pseudo-contractive mapping | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-CONVERGENCE THEOREMS | Constrictions | Mapping | Banach space | Inequalities | Convergence

uniformly convex Banach space | Analysis | Mathematics, general | nonexpansive mapping | Mann iteration | Mathematics | Applications of Mathematics | strictly pseudo-contractive mapping | MATHEMATICS | MATHEMATICS, APPLIED | WEAK-CONVERGENCE THEOREMS | Constrictions | Mapping | Banach space | Inequalities | Convergence

Journal Article

Kragujevac Journal of Mathematics, ISSN 1450-9628, 2016, Volume 40, Issue 2, pp. 272 - 279

Journal Article

Journal of Convex Analysis, ISSN 0944-6532, 2006, Volume 13, Issue 3-4, pp. 525 - 559

The aim of the paper is to extend to the setting of uniformly convex Banach spaces the results obtained for prox-regular sets in Hilbert spaces....

Variational analysis | Metric projection mapping | Proximal normal | Uniformly convex Banach space | Distance function | Prox-regular set | uniformly convex Banach space | HILBERT-SPACES | distance function | metric projection mapping | INEQUALITIES | DIFFERENTIABILITY | variational analysis | proximal normal | prox-regular set | LOWER NICE FUNCTIONS | METRIC PROJECTIONS | MATHEMATICS | CLOSED-SETS | BOUNDARIES | INTEGRATION | SUBDIFFERENTIALS

Variational analysis | Metric projection mapping | Proximal normal | Uniformly convex Banach space | Distance function | Prox-regular set | uniformly convex Banach space | HILBERT-SPACES | distance function | metric projection mapping | INEQUALITIES | DIFFERENTIABILITY | variational analysis | proximal normal | prox-regular set | LOWER NICE FUNCTIONS | METRIC PROJECTIONS | MATHEMATICS | CLOSED-SETS | BOUNDARIES | INTEGRATION | SUBDIFFERENTIALS

Journal Article

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