European Journal of Operational Research, ISSN 0377-2217, 06/2018, Volume 267, Issue 2, pp. 667 - 675

•We discuss capital allocation rules for quite general risk measures.•Our capital allocation rules are inspired by the Aumann–Shapley principle.•Our approach...

Capital allocation rules | Gateaux differential | Risk management | Aumann–Shapley value | Convex/quasi-convex risk measures | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVEX | Aumann-Shapley value | REPRESENTATION | OPTIMIZATION

Capital allocation rules | Gateaux differential | Risk management | Aumann–Shapley value | Convex/quasi-convex risk measures | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVEX | Aumann-Shapley value | REPRESENTATION | OPTIMIZATION

Journal Article

International Journal of Pure and Applied Mathematics, ISSN 1311-8080, 2013, Volume 83, Issue 3, pp. 465 - 475

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2019, Volume 478, Issue 2, pp. 526 - 538

This article is devoted to smooth approximation of convex functions on Banach spaces with smooth norm. We prove that if X⁎ is a smooth space and f is a...

Convex function | Gâteaux differentiable | Smooth space | Uniform approximation | MATHEMATICS | MATHEMATICS, APPLIED | VARIATIONAL PRINCIPLE | DIFFERENTIABILITY | Gateaux differentiable

Convex function | Gâteaux differentiable | Smooth space | Uniform approximation | MATHEMATICS | MATHEMATICS, APPLIED | VARIATIONAL PRINCIPLE | DIFFERENTIABILITY | Gateaux differentiable

Journal Article

Studia Scientiarum Mathematicarum Hungarica, ISSN 0081-6906, 03/2014, Volume 51, Issue 1, pp. 17 - 23

Applying certain convexity arguments we investigate the existence of a classical solution for a Dirichlet problem for which the Euler action functional is not...

Dirichlet Problem | coercivity | 58E30 | Fenchel-Young conjugate | Primary 34B15 | MATHEMATICS | Dirichlet problem | Convexity | Gateaux | Mathematical analysis | Coercive force

Dirichlet Problem | coercivity | 58E30 | Fenchel-Young conjugate | Primary 34B15 | MATHEMATICS | Dirichlet problem | Convexity | Gateaux | Mathematical analysis | Coercive force

Journal Article

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

Colloquium Mathematicum, ISSN 0010-1354, 2013, Volume 131, Issue 1, pp. 29 - 40

Journal Article

Bulletin of the Brazilian Mathematical Society, ISSN 1678-7544, 09/2009, Volume 40, Issue 3, pp. 371 - 380

Given real Banach spaces X and Y, let C (wbu) (1) (X, Y) be the space, introduced by R.M. Aron and J.B. Prolla, of C (1) mappings from X into Y such that the...

Factorization of differentiable mappings | Gâteaux differentiable mapping | Fréchet differentiable mapping | Weakly uniformly continuous mapping on bounded sets | MATHEMATICS | factorization of differentiable mappings | Frechet differentiable mapping | weakly uniformly continuous mapping on bounded sets | Gateaux differentiable mapping

Factorization of differentiable mappings | Gâteaux differentiable mapping | Fréchet differentiable mapping | Weakly uniformly continuous mapping on bounded sets | MATHEMATICS | factorization of differentiable mappings | Frechet differentiable mapping | weakly uniformly continuous mapping on bounded sets | Gateaux differentiable mapping

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

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2016, Volume 434, Issue 1, pp. 182 - 190

In this paper, author proves that if X1 and X2 are Gâteaux differentiable space, then X1 and X2 have the ball-covering property if and only if (X1×X2,‖⋅‖p) and...

Gâteaux differentiable space | Ball-covering property | Convex function | MATHEMATICS | MATHEMATICS, APPLIED | MAPPINGS | WEAK ASPLUND SPACES | Gateaux differentiable space | CONVEX-FUNCTIONS | FRECHET DIFFERENTIABILITY | Bisphenol-A

Gâteaux differentiable space | Ball-covering property | Convex function | MATHEMATICS | MATHEMATICS, APPLIED | MAPPINGS | WEAK ASPLUND SPACES | Gateaux differentiable space | CONVEX-FUNCTIONS | FRECHET DIFFERENTIABILITY | Bisphenol-A

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

Mathematical Notes, ISSN 0001-4346, 3/2013, Volume 93, Issue 3, pp. 593 - 606

For the simplest heat equation with power nonlinearity, the dependence of the solution of the corresponding boundary-value problem on the constant term of the...

Lagrange optimality principle | Gâteaux differentiability | heat equation with power nonlinearity | Mathematics, general | optimal control | Mathematics | nonlinear evolution system | TRANSFORMATION | MATHEMATICS | PARABOLIC EQUATIONS | Gateaux differentiability | SPATIAL ARGUMENTS | BANACH-SPACE

Lagrange optimality principle | Gâteaux differentiability | heat equation with power nonlinearity | Mathematics, general | optimal control | Mathematics | nonlinear evolution system | TRANSFORMATION | MATHEMATICS | PARABOLIC EQUATIONS | Gateaux differentiability | SPATIAL ARGUMENTS | BANACH-SPACE

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, 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

Advances in Pure and Applied Mathematics, ISSN 1867-1152, 07/2018, Volume 9, Issue 3, pp. 167 - 184

In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is...

convex minimization problem | Legendre functions | Gâteaux differentiable function | Bregman distance | strong convergence | Bregman projection | Fréchet differentiable functions | 47H09 | variational inequality, reflexive Banach space | 47J05 | 47J25 | resolvent | 47H06 | reffexive Banach space | variational inequality | Iterative algorithms | Error analysis | Banach spaces | Banach space | Optimization

convex minimization problem | Legendre functions | Gâteaux differentiable function | Bregman distance | strong convergence | Bregman projection | Fréchet differentiable functions | 47H09 | variational inequality, reflexive Banach space | 47J05 | 47J25 | resolvent | 47H06 | reffexive Banach space | variational inequality | Iterative algorithms | Error analysis | Banach spaces | Banach space | Optimization

Journal Article

Studia Mathematica, ISSN 0039-3223, 2018, Volume 241, Issue 1, pp. 71 - 86

We use the smooth variational principle and a standard renorming to give a short direct proof of the classical Bishop-Phelps-Bollobas theorem on the density of...

Bishop-Phelps-Bollobás theorem | Weakly compactly generated spaces | Smooth variational principle | Gâteaux differentiable norm | Norm-attaining functionals | MATHEMATICS | Gateaux differentiable norm | ANALYTIC SETS | TOPOLOGICAL PROPERTIES | Bishop Phelps Bollobas theorem | BANACH-SPACES | PROPERTY | norm-attaining functionals | weakly compactly generated spaces | smooth variational principle | CONVEX-FUNCTIONS

Bishop-Phelps-Bollobás theorem | Weakly compactly generated spaces | Smooth variational principle | Gâteaux differentiable norm | Norm-attaining functionals | MATHEMATICS | Gateaux differentiable norm | ANALYTIC SETS | TOPOLOGICAL PROPERTIES | Bishop Phelps Bollobas theorem | BANACH-SPACES | PROPERTY | norm-attaining functionals | weakly compactly generated spaces | smooth variational principle | CONVEX-FUNCTIONS

Journal Article

Optimization, ISSN 0233-1934, 02/2018, Volume 67, Issue 2, pp. 329 - 340

The aim of the paper is to characterize weakly sharp solutions of a variational inequality problem. In particular, we present weak sharpness results by using...

convergence of an algorithm | gap functions | gâteaux differentiable | error bound | Variational inequality | locally Lipschitz property | weakly sharp solution | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | gateaux differentiable | TERMINATION | GAP FUNCTION | Optimization algorithms | Algorithms | Sharpness | Portfolio management | Inequality

convergence of an algorithm | gap functions | gâteaux differentiable | error bound | Variational inequality | locally Lipschitz property | weakly sharp solution | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | gateaux differentiable | TERMINATION | GAP FUNCTION | Optimization algorithms | Algorithms | Sharpness | Portfolio management | Inequality

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

19.
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

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 10/2015, Volume 92, Issue 3, pp. 457 - 462

A nonreflexive Banach space may have a weakly uniformly rotund dual. The aim of this paper is to determine alternative characterisations and study further...

renormings | reflexivity | Gâteaux and uniformly Gâteaux differentiable | weak and weak∗ uniform rotundity | MATHEMATICS | Gateaux and uniformly Gateaux differentiable | weak and weak uniform rotundity

renormings | reflexivity | Gâteaux and uniformly Gâteaux differentiable | weak and weak∗ uniform rotundity | MATHEMATICS | Gateaux and uniformly Gateaux differentiable | weak and weak uniform rotundity

Journal Article

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