Transactions of the American Mathematical Society, ISSN 0002-9947, 08/2014, Volume 366, Issue 8, pp. 4299 - 4322

Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators...

Social classes | Mathematical monotonicity | Normed spaces | Applied mathematics | Diagonal lemma | Geodesy | Hilbert spaces | Convexity | Banach space | Curvature | Firmly nonexpansive mappings | Picard iterates | Proof mining | Geodesic spaces | Asymptotic regularity | Effective bounds | Δ-convergence | Minimization problems | Uniform convexity | proof mining | geodesic spaces | MONOTONE VECTOR-FIELDS | ACCRETIVE-OPERATORS | PROXIMAL POINT ALGORITHM | uniform convexity | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | NONLINEAR OPERATORS | Delta-convergence | ITERATIONS | REGULARITY | THEOREMS | asymptotic regularity | SETS | CONVERGENCE | minimization problems | effective bounds

Social classes | Mathematical monotonicity | Normed spaces | Applied mathematics | Diagonal lemma | Geodesy | Hilbert spaces | Convexity | Banach space | Curvature | Firmly nonexpansive mappings | Picard iterates | Proof mining | Geodesic spaces | Asymptotic regularity | Effective bounds | Δ-convergence | Minimization problems | Uniform convexity | proof mining | geodesic spaces | MONOTONE VECTOR-FIELDS | ACCRETIVE-OPERATORS | PROXIMAL POINT ALGORITHM | uniform convexity | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | NONLINEAR OPERATORS | Delta-convergence | ITERATIONS | REGULARITY | THEOREMS | asymptotic regularity | SETS | CONVERGENCE | minimization problems | effective bounds

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2015, Volume 167, Issue 2, pp. 409 - 429

... of results proved recently in this direction. For this purpose, we analyze the asymptotic behavior of compositions of finitely many firmly nonexpansive mappings focusing...

p$$ p -Uniformly convex geodesic space | 53C23 | Mathematics | Theory of Computation | Optimization | CAT $$(\kappa )$$ ( κ ) space | Convex feasibility problem | Calculus of Variations and Optimal Control; Optimization | Convex optimization | Firmly nonexpansive mapping | 47H09 | 49M27 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | CAT(κ) space | p-Uniformly convex geodesic space | MATHEMATICS, APPLIED | INEQUALITIES | METRIC-SPACES | GEODESIC SPACES | UNIFORM CONVEXITY | CAT(kappa) space | PROXIMAL POINT ALGORITHM | VECTOR-FIELDS | NONLINEAR OPERATORS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BANACH-SPACES | HADAMARD SPACES | CONVERGENCE | Minimization | Mapping | Asymptotic properties | Regularity | Convergence

p$$ p -Uniformly convex geodesic space | 53C23 | Mathematics | Theory of Computation | Optimization | CAT $$(\kappa )$$ ( κ ) space | Convex feasibility problem | Calculus of Variations and Optimal Control; Optimization | Convex optimization | Firmly nonexpansive mapping | 47H09 | 49M27 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | CAT(κ) space | p-Uniformly convex geodesic space | MATHEMATICS, APPLIED | INEQUALITIES | METRIC-SPACES | GEODESIC SPACES | UNIFORM CONVEXITY | CAT(kappa) space | PROXIMAL POINT ALGORITHM | VECTOR-FIELDS | NONLINEAR OPERATORS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BANACH-SPACES | HADAMARD SPACES | CONVERGENCE | Minimization | Mapping | Asymptotic properties | Regularity | Convergence

Journal Article

Carpathian Journal of Mathematics, ISSN 1584-2851, 1/2016, Volume 32, Issue 1, pp. 13 - 28

In 2011 Aoyama and Kohsaka introduced the α-nonexpansive mappings. Here we present a further study about them and their relationships with other classes...

Unit ball | Ergodic theory | Mathematical theorems | Real numbers | Diagonal lemma | Hilbert spaces | Convexity | Banach space | Fixed point property | Hybrid mappings | Firmly nonexpansive mappings | Nonspreading mappings | Fixed point theorem nonexpansive mappings | MATHEMATICS | fixed point theorem nonexpansive mappings | NONLINEAR MAPPINGS | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | hybrid mappings | nonspreading mappings | ERGODIC-THEOREMS

Unit ball | Ergodic theory | Mathematical theorems | Real numbers | Diagonal lemma | Hilbert spaces | Convexity | Banach space | Fixed point property | Hybrid mappings | Firmly nonexpansive mappings | Nonspreading mappings | Fixed point theorem nonexpansive mappings | MATHEMATICS | fixed point theorem nonexpansive mappings | NONLINEAR MAPPINGS | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | hybrid mappings | nonspreading mappings | ERGODIC-THEOREMS

Journal Article

JOURNAL OF CONVEX ANALYSIS, ISSN 0944-6532, 2019, Volume 26, Issue 3, pp. 911 - 924

We show that in the framework of CAT(0) spaces, any convex combination of two mappings which are firmly nonexpansive - or which satisfy the more general...

MATHEMATICS | proof mining | firmly nonexpansive mappings | asymptotic regularity | averaged projections | convex optimization | CONVERGENCE | CAT spaces

MATHEMATICS | proof mining | firmly nonexpansive mappings | asymptotic regularity | averaged projections | convex optimization | CONVERGENCE | CAT spaces

Journal Article

Set-valued and variational analysis, ISSN 1877-0541, 2017, Volume 26, Issue 4, pp. 1009 - 1078

.... The paper consists of three parts. In the first part, we study basic properties of subgradient projectors and give characterizations when a subgradient projector is a cutter, a local cutter, or a quasi-nonexpansive mapping...

Cutter | Linear cutter | Projection | Mathematics | Local cutter | Local Lipschitz function | Optimization | Local quasi-firmly nonexpansive mapping | Secondary 49J53 | Averaged mapping | Prox-regular function | Essentially strictly differentiable function | Prox-bounded | 47H09 | 47H05 | ( C , ε )-firmly nonexpansive mapping | 47H04 | Quasi-nonexpansive mapping | Linear subgradient projection operator | Quasi-firmly nonexpansive mapping | Moreau envelope | Subdifferentiable function | Approximately convex function | Limiting subgradient | Proximal mapping | Local quasi-nonexpansive mapping | Subgradient projection operator | Analysis | Primary 49J52 | Linear firmly nonexpansive mapping | Fixed point | (C,ε)-firmly nonexpansive mapping | MATHEMATICS, APPLIED | CONVEX-OPTIMIZATION | LEVEL SET | CONVERGENCE | EFFICIENCY | PROX-REGULAR FUNCTIONS | (C,epsilon)-firmly nonexpansive mapping | SUBDIFFERENTIALS | Projectors

Cutter | Linear cutter | Projection | Mathematics | Local cutter | Local Lipschitz function | Optimization | Local quasi-firmly nonexpansive mapping | Secondary 49J53 | Averaged mapping | Prox-regular function | Essentially strictly differentiable function | Prox-bounded | 47H09 | 47H05 | ( C , ε )-firmly nonexpansive mapping | 47H04 | Quasi-nonexpansive mapping | Linear subgradient projection operator | Quasi-firmly nonexpansive mapping | Moreau envelope | Subdifferentiable function | Approximately convex function | Limiting subgradient | Proximal mapping | Local quasi-nonexpansive mapping | Subgradient projection operator | Analysis | Primary 49J52 | Linear firmly nonexpansive mapping | Fixed point | (C,ε)-firmly nonexpansive mapping | MATHEMATICS, APPLIED | CONVEX-OPTIMIZATION | LEVEL SET | CONVERGENCE | EFFICIENCY | PROX-REGULAR FUNCTIONS | (C,epsilon)-firmly nonexpansive mapping | SUBDIFFERENTIALS | Projectors

Journal Article

Optimization letters, ISSN 1862-4480, 2018, Volume 12, Issue 7, pp. 1465 - 1474

Maximally monotone operators and firmly nonexpansive mappings play key roles in modern optimization and nonlinear analysis...

Maximally monotone operator | Computational Intelligence | Resolvent | Operations Research/Decision Theory | Firmly nonexpansive mapping | Asymptotically regular | Mathematics | Numerical and Computational Physics, Simulation | Minimal displacement vector | Optimization | Nonexpansive mapping | MATHEMATICS, APPLIED | ALGORITHM | SUM | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SETS | HILBERT-SPACE | MONOTONE-OPERATORS

Maximally monotone operator | Computational Intelligence | Resolvent | Operations Research/Decision Theory | Firmly nonexpansive mapping | Asymptotically regular | Mathematics | Numerical and Computational Physics, Simulation | Minimal displacement vector | Optimization | Nonexpansive mapping | MATHEMATICS, APPLIED | ALGORITHM | SUM | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SETS | HILBERT-SPACE | MONOTONE-OPERATORS

Journal Article

Fixed point theory and applications (Hindawi Publishing Corporation), ISSN 1687-1812, 2012, Volume 2012, Issue 1, pp. 1 - 11

Because of Minty's classical correspondence between firmly nonexpansive mappings and maximally monotone operators, the notion of a firmly nonexpansive mapping has proven to be of basic importance...

Mathematical and Computational Biology | strongly nonexpansive mapping | nonexpansive mapping | Mathematics | Topology | maximally monotone operator | firmly nonexpansive mapping | Analysis | asymptotic regularity | Mathematics, general | Hilbert space | Applications of Mathematics | Differential Geometry | resolvent | Maximally monotone operator | Strongly nonexpansive mapping | Resolvent | Firmly nonexpansive mapping | Asymptotic regularity | Nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | BEHAVIOR | HILBERT-SPACE | MONOTONE-OPERATORS | Fixed point theory | Usage | Research | Point mappings (Mathematics) | Mathematical optimization | Operators | Approximation | Equivalence | Asymptotic properties | Mathematical analysis | Classification | Mapping | Optimization

Mathematical and Computational Biology | strongly nonexpansive mapping | nonexpansive mapping | Mathematics | Topology | maximally monotone operator | firmly nonexpansive mapping | Analysis | asymptotic regularity | Mathematics, general | Hilbert space | Applications of Mathematics | Differential Geometry | resolvent | Maximally monotone operator | Strongly nonexpansive mapping | Resolvent | Firmly nonexpansive mapping | Asymptotic regularity | Nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | BEHAVIOR | HILBERT-SPACE | MONOTONE-OPERATORS | Fixed point theory | Usage | Research | Point mappings (Mathematics) | Mathematical optimization | Operators | Approximation | Equivalence | Asymptotic properties | Mathematical analysis | Classification | Mapping | Optimization

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 08/2013, Volume 87, pp. 102 - 115

We further study averaged and firmly nonexpansive mappings in the setting of geodesic spaces with a main focus on the asymptotic behavior of their Picard iterates...

Geodesic space | Asymptotic regularity | Convex feasibility problem | Averaged mapping | Firmly nonexpansive mapping | Proof mining | MATHEMATICS, APPLIED | ALGORITHMS | CONTRACTIONS | MATHEMATICS | PROJECTION | SEMIGROUPS | ITERATIONS | REGULARITY | CONVERGENCE | OPERATORS | RANGE | Algorithms | Mining | Asymptotic properties | Proving | Nonlinearity | Feasibility | Mapping | Regularity

Geodesic space | Asymptotic regularity | Convex feasibility problem | Averaged mapping | Firmly nonexpansive mapping | Proof mining | MATHEMATICS, APPLIED | ALGORITHMS | CONTRACTIONS | MATHEMATICS | PROJECTION | SEMIGROUPS | ITERATIONS | REGULARITY | CONVERGENCE | OPERATORS | RANGE | Algorithms | Mining | Asymptotic properties | Proving | Nonlinearity | Feasibility | Mapping | Regularity

Journal Article

Numerical algorithms, ISSN 1572-9265, 2015, Volume 72, Issue 2, pp. 297 - 323

In this paper we consider the common fixed point problem for a finite family of quasi-nonexpansive mappings U i : ℋ → ℋ $U_{i}\colon \mathcal H\rightarrow \mathcal H$ , where i ∈ I := {1,…, M}, M≥1, and ℋ $\mathcal H...

Nonexpansive operator | Cutter | Common fixed point problem | Theory of Computation | Intermittent control | Perturbation resilience | Cyclic control | Superiorization | Algebra | Convex feasibility problem | 65F10 | Subgradient projection | Computer Science | 47H09 | 65J99 | Almost cyclic control | 47J25 | Firmly nonexpansive operator | 46N10 | Block iterative algorithms | Numeric Computing | 47H10 | Algorithms | Numerical Analysis | String averaging | Quasi-nonexpansive operator | 47N10 | 46N40 | MATHEMATICS, APPLIED | CONVEX FEASIBILITY | VARIATIONAL INEQUALITY PROBLEM | ALGORITHMS | BANACH | CONVERGENCE THEOREMS | ITERATIVE PROJECTION METHODS | RANDOM PRODUCTS | OPERATORS | Analysis

Nonexpansive operator | Cutter | Common fixed point problem | Theory of Computation | Intermittent control | Perturbation resilience | Cyclic control | Superiorization | Algebra | Convex feasibility problem | 65F10 | Subgradient projection | Computer Science | 47H09 | 65J99 | Almost cyclic control | 47J25 | Firmly nonexpansive operator | 46N10 | Block iterative algorithms | Numeric Computing | 47H10 | Algorithms | Numerical Analysis | String averaging | Quasi-nonexpansive operator | 47N10 | 46N40 | MATHEMATICS, APPLIED | CONVEX FEASIBILITY | VARIATIONAL INEQUALITY PROBLEM | ALGORITHMS | BANACH | CONVERGENCE THEOREMS | ITERATIVE PROJECTION METHODS | RANDOM PRODUCTS | OPERATORS | Analysis

Journal Article

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Firmly Nonexpansive Mappings and Maximally Monotone Operators: Correspondence and Duality

Set-valued and variational analysis, ISSN 1877-0541, 2011, Volume 20, Issue 1, pp. 131 - 153

The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximally monotone operators due to Minty...

Banach contraction | 52A41 | Proximal map | Subdifferential operator | Mathematics | Nonexpansive mapping | Geometry | Maximally monotone operator | Rectangular | Resolvent | Secondary 26B25 | Primary 47H05 | 90C25 | Analysis | Firmly nonexpansive mapping | 47H09 | Convex function | Hilbert space | Legendre function | Paramonotone | Fixed point | MATHEMATICS, APPLIED | FITZPATRICK FUNCTIONS | EXTENSION | NONLINEAR OPERATORS | CONVERGENCE

Banach contraction | 52A41 | Proximal map | Subdifferential operator | Mathematics | Nonexpansive mapping | Geometry | Maximally monotone operator | Rectangular | Resolvent | Secondary 26B25 | Primary 47H05 | 90C25 | Analysis | Firmly nonexpansive mapping | 47H09 | Convex function | Hilbert space | Legendre function | Paramonotone | Fixed point | MATHEMATICS, APPLIED | FITZPATRICK FUNCTIONS | EXTENSION | NONLINEAR OPERATORS | CONVERGENCE

Journal Article

Mathematical programming, ISSN 1436-4646, 2013, Volume 139, Issue 1-2, pp. 55 - 70

We study nearly equal and nearly convex sets, ranges of maximally monotone operators, and ranges and fixed points of convex combinations of firmly nonexpansive mappings...

52A20 | Theoretical, Mathematical and Computational Physics | Asymptotic regularity | Mathematics | Monotone operator | Mathematical Methods in Physics | 47H10 | Resolvent | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Nearly convex set | 90C25 | Numerical Analysis | Firmly nonexpansive mapping | 47H09 | Combinatorics | 47H05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | PROXIMAL AVERAGE | DUALITY | Studies | Mapping | Asymptotic methods | Analysis | Mathematical programming | Operators | Convexity | Asymptotic properties | Sums

52A20 | Theoretical, Mathematical and Computational Physics | Asymptotic regularity | Mathematics | Monotone operator | Mathematical Methods in Physics | 47H10 | Resolvent | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Nearly convex set | 90C25 | Numerical Analysis | Firmly nonexpansive mapping | 47H09 | Combinatorics | 47H05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | PROXIMAL AVERAGE | DUALITY | Studies | Mapping | Asymptotic methods | Analysis | Mathematical programming | Operators | Convexity | Asymptotic properties | Sums

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 13, pp. 4387 - 4391

We introduce the class of α -nonexpansive mappings in Banach spaces. This class contains the class of nonexpansive mappings and is related to the class of firmly nonexpansive mappings in Banach spaces...

Fixed point theorem | Nonspreading mapping | Firmly nonexpansive mapping | Nonexpansive mapping | Hybrid mapping | MATHEMATICS | NONLINEAR MAPPINGS | MATHEMATICS, APPLIED | OPERATORS | Nonlinearity | Theorems | Fixed points (mathematics) | Mapping | Banach space

Fixed point theorem | Nonspreading mapping | Firmly nonexpansive mapping | Nonexpansive mapping | Hybrid mapping | MATHEMATICS | NONLINEAR MAPPINGS | MATHEMATICS, APPLIED | OPERATORS | Nonlinearity | Theorems | Fixed points (mathematics) | Mapping | Banach space

Journal Article

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

We introduce the concept of ψ-firmly nonexpansive mapping, which includes a firmly nonexpansive mapping as a special case in a uniformly convex Banach space...

ψ -firmly nonexpansive mappings | fixed points | Picard iteration | Mathematical and Computational Biology | Analysis | Mathematics, general | reflexive Banach spaces | Mathematics | Applications of Mathematics | Topology | Differential Geometry | ψ-firmly nonexpansive mappings | Fixed points | Reflexive Banach spaces | NON-EXPANSIVE MAPPINGS | MATHEMATICS, APPLIED | WEAK CONVERGENCE | MATHEMATICS | CONVERGENCE THEOREMS | BANACH-SPACES | psi-firmly nonexpansive mappings | COMPACTNESS | NONLINEAR CONTRACTIONS | OPERATORS | Fixed point theory | Usage | Approximation theory | Banach spaces | Contraction operators | Fixed points (mathematics) | Mapping | Approximation | Picard iterations | Banach space | Mathematical analysis

ψ -firmly nonexpansive mappings | fixed points | Picard iteration | Mathematical and Computational Biology | Analysis | Mathematics, general | reflexive Banach spaces | Mathematics | Applications of Mathematics | Topology | Differential Geometry | ψ-firmly nonexpansive mappings | Fixed points | Reflexive Banach spaces | NON-EXPANSIVE MAPPINGS | MATHEMATICS, APPLIED | WEAK CONVERGENCE | MATHEMATICS | CONVERGENCE THEOREMS | BANACH-SPACES | psi-firmly nonexpansive mappings | COMPACTNESS | NONLINEAR CONTRACTIONS | OPERATORS | Fixed point theory | Usage | Approximation theory | Banach spaces | Contraction operators | Fixed points (mathematics) | Mapping | Approximation | Picard iterations | Banach space | Mathematical analysis

Journal Article

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Halpern-type iterations for strongly relatively nonexpansive mappings in Banach spaces

Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 62, Issue 12, pp. 4656 - 4666

.... We also modify Halpern’s iteration for finding a fixed point of a strongly relatively nonexpansive mapping in a Banach space...

Strongly relatively nonexpansive mapping | Maximal monotone operator | Strongly generalized nonexpansive mapping | Firmly generalized nonexpansive type mapping | Relatively nonexpansive mapping | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | ALGORITHM | STRONG-CONVERGENCE THEOREMS | FAMILY | WEAK | NONLINEAR MAPPINGS | PROJECTION | FIXED-POINT THEOREMS | Operators | Theorems | Analogue | Mapping | Mathematical models | Banach space | Iterative methods | Convergence

Strongly relatively nonexpansive mapping | Maximal monotone operator | Strongly generalized nonexpansive mapping | Firmly generalized nonexpansive type mapping | Relatively nonexpansive mapping | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | ALGORITHM | STRONG-CONVERGENCE THEOREMS | FAMILY | WEAK | NONLINEAR MAPPINGS | PROJECTION | FIXED-POINT THEOREMS | Operators | Theorems | Analogue | Mapping | Mathematical models | Banach space | Iterative methods | Convergence

Journal Article

Journal of fixed point theory and applications, ISSN 1661-7746, 2015, Volume 18, Issue 2, pp. 297 - 307

In 1971, Pazy [Israel J. Math. 9 (1971), 235–240] presented a beautiful trichotomy result concerning the asymptotic behaviour of the iterates of a nonexpansive mapping...

firmly nonexpansive mapping | Mathematical Methods in Physics | Secondary 90C25 | Cosmic convergence | projection operator | Analysis | Primary 47H09 | Mathematics, general | nonexpansive mapping | Mathematics | Poincaré metric | MATHEMATICS, APPLIED | ALGORITHM | ACCRETIVE-OPERATORS | Poincare metric | CONTRACTIONS | MATHEMATICS | SEMIGROUPS | MAPS | SETS | HILBERT-SPACE | RANGE | Computer science | Resveratrol

firmly nonexpansive mapping | Mathematical Methods in Physics | Secondary 90C25 | Cosmic convergence | projection operator | Analysis | Primary 47H09 | Mathematics, general | nonexpansive mapping | Mathematics | Poincaré metric | MATHEMATICS, APPLIED | ALGORITHM | ACCRETIVE-OPERATORS | Poincare metric | CONTRACTIONS | MATHEMATICS | SEMIGROUPS | MAPS | SETS | HILBERT-SPACE | RANGE | Computer science | Resveratrol

Journal Article

Optimization, ISSN 1029-4945, 2016, Volume 66, Issue 8, pp. 1291 - 1299

... to the composition of two firmly nonexpansive mappings.

CAT space | convex optimization | Firmly nonexpansive mapping | asymptotic regularity | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GEODESIC SPACES | BANACH-SPACES | BEHAVIOR | FIRMLY NONEXPANSIVE-MAPPINGS | Mining | Mapping | Asymptotic properties | Metastable state | Regularity | Optimization

CAT space | convex optimization | Firmly nonexpansive mapping | asymptotic regularity | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GEODESIC SPACES | BANACH-SPACES | BEHAVIOR | FIRMLY NONEXPANSIVE-MAPPINGS | Mining | Mapping | Asymptotic properties | Metastable state | Regularity | Optimization

Journal Article

SIAM journal on optimization, ISSN 1095-7189, 2015, Volume 25, Issue 2, pp. 1064 - 1082

The subgradient projector is of considerable importance in convex optimization because it plays the key role in Polyak's seminal work-and the many papers it...

Fréchet differentiability | Gâteaux differentiability | Yamagishi-Yamada operator | Firmly nonexpansive mapping | Convex function | Monotone operator | Subgradient projector | Nonexpansive mapping | MATHEMATICS, APPLIED | subgradient projector | convex function | nonexpansive mapping | Gateaux differentiability | monotone operator | firmly nonexpansive mapping | LEVEL SET | CONVEX | CONVERGENCE | QUASI-NONEXPANSIVE-MAPPINGS | Frechet differentiability | POINTS

Fréchet differentiability | Gâteaux differentiability | Yamagishi-Yamada operator | Firmly nonexpansive mapping | Convex function | Monotone operator | Subgradient projector | Nonexpansive mapping | MATHEMATICS, APPLIED | subgradient projector | convex function | nonexpansive mapping | Gateaux differentiability | monotone operator | firmly nonexpansive mapping | LEVEL SET | CONVEX | CONVERGENCE | QUASI-NONEXPANSIVE-MAPPINGS | Frechet differentiability | POINTS

Journal Article

Mathematical Communications, ISSN 1331-0623, 06/2011, Volume 16, Issue 1, pp. 251 - 264

In this paper, two examples of quasi-firmly type nonexpansive mappings are given to prove that the concept is different from nonexpansive mapping...

Krasnosel- skii-mann iteration | Ishikawa-type iteration | Quasi-firmly type nonexpansive mappings | MATHEMATICS | ITERATIVE PROCESS | MATHEMATICS, APPLIED | quasi-firmly type nonexpansive mappings | BANACH-SPACES | SETS | Krasnoselskii-Mann iteration | WEAK CONVERGENCE | KRASNOSELSKI | FIXED-POINTS

Krasnosel- skii-mann iteration | Ishikawa-type iteration | Quasi-firmly type nonexpansive mappings | MATHEMATICS | ITERATIVE PROCESS | MATHEMATICS, APPLIED | quasi-firmly type nonexpansive mappings | BANACH-SPACES | SETS | Krasnoselskii-Mann iteration | WEAK CONVERGENCE | KRASNOSELSKI | FIXED-POINTS

Journal Article

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Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2007, Volume 135, Issue 1, pp. 135 - 139

.... In the same spirit, we provide a new proof of an extension result for firmly nonexpansive mappings with an optimally localized range.

Hilbert spaces | Mathematical functions | Mathematical duality | Mathematical theorems | Banach space | Fenchel duality | Kirszbraun-Valentine theorem | Fitzpatrick function | Firmly nonexpansive mapping | firmly nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | fenchel duality

Hilbert spaces | Mathematical functions | Mathematical duality | Mathematical theorems | Banach space | Fenchel duality | Kirszbraun-Valentine theorem | Fitzpatrick function | Firmly nonexpansive mapping | firmly nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | fenchel duality

Journal Article

Journal of Nonlinear and Convex Analysis, ISSN 1345-4773, 01/2014, Volume 15, Issue 1, pp. 61 - 87

Firmly nonexpansive mappings play an important role in nonlinear analysis due to their correspondence with maximal monotone operators...

Geodesic space | Resolvent | Picard iterates | Firmly nonexpansive mapping | Δ-convergence | Asymptotic regularity | Fixed point | Uniform convexity | CONVEX FUNCTIONALS | MATHEMATICS, APPLIED | APPROXIMATION | NON-LINEAR SEMIGROUPS | MONOTONE VECTOR-FIELDS | COACCRETIVE OPERATORS | geodesic space | uniform convexity | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | NONLINEAR OPERATORS | Delta-convergence | CONVERGENCE THEOREMS | fixed point | asymptotic regularity | WEAK-CONVERGENCE | resolvent | FIXED-POINTS

Geodesic space | Resolvent | Picard iterates | Firmly nonexpansive mapping | Δ-convergence | Asymptotic regularity | Fixed point | Uniform convexity | CONVEX FUNCTIONALS | MATHEMATICS, APPLIED | APPROXIMATION | NON-LINEAR SEMIGROUPS | MONOTONE VECTOR-FIELDS | COACCRETIVE OPERATORS | geodesic space | uniform convexity | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | NONLINEAR OPERATORS | Delta-convergence | CONVERGENCE THEOREMS | fixed point | asymptotic regularity | WEAK-CONVERGENCE | resolvent | FIXED-POINTS

Journal Article

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