Weak sharpness for solutions of nonsmooth variational inequalities and applications

In this paper, we first give some new characterizations of weak sharpness of the solution set of nonsmoothvariational inequalities in terms of partial subdiferentials/Gˆateaux derivatives of involving bifunctions. Asapplications, we use a new characterization to establish sufficient conditions for guaranteeing finite terminationof an arbitrary algorithm solving nonsmooth variational inequalities under the weak sharpness assumption

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A generalized cyclic iterative method for solving variational inequalities over the solution set of a split common fixed point problem

Numerical Algorithms ◽

10.1007/s11075-021-01252-0 ◽

2022 ◽

Author(s):

Simeon Reich ◽

Truong Minh Tuyen

Keyword(s):

Fixed Point ◽

Iterative Method ◽

Variational Inequalities ◽

Common Fixed Point ◽

Fixed Point Problem ◽

Solution Set ◽

Point Problem ◽

Common Fixed Point Problem ◽

Split Common Fixed Point

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Generalized Knaster-Kuratowski-Mazurkiewicz type theorems and applications to minimax inequalities

Science and Technology Development Journal ◽

10.32508/stdj.v20ik2.459 ◽

2017 ◽

Vol 20 (K2) ◽

pp. 131-140

Author(s):

Linh Manh Ha

Keyword(s):

Variational Inequalities ◽

Equilibrium Problems ◽

Applied Mathematics ◽

Sufficient Conditions ◽

Topological Spaces ◽

Minimax Theorems ◽

Minimax Inequalities ◽

Special Cases ◽

Kkm Mappings ◽

Definition Of

Knaster-Kuratowski-Mazurkiewicz type theorems play an important role in nonlinear analysis, optimization, and applied mathematics. Since the first well-known result, many international efforts have been made to develop sufficient conditions for the existence of points intersection (and their applications) in increasingly general settings: Gconvex spaces [21, 23], L-convex spaces [12], and FCspaces [8, 9]. Applications of Knaster-Kuratowski-Mazurkiewicz type theorems, especially in existence studies for variational inequalities, equilibrium problems and more general settings have been obtained by many authors, see e.g. recent papers [1, 2, 3, 8, 18, 24, 26] and the references therein. In this paper we propose a definition of generalized KnasterKuratowski-Mazurkiewicz mappings to encompass R-KKM mappings [5], L-KKM mappings [11], T-KKM mappings [18, 19], and many recent existing mappings. Knaster-KuratowskiMazurkiewicz type theorems are established in general topological spaces to generalize known results. As applications, we develop in detail general types of minimax theorems. Our results are shown to improve or include as special cases several recent ones in the literature.

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Sequential Derivatives of Nonlinearq-Difference Equations with Three-Pointq-Integral Boundary Conditions

Journal of Applied Mathematics ◽

10.1155/2013/605169 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

Nittaya Pongarm ◽

Suphawat Asawasamrit ◽

Jessada Tariboon

Keyword(s):

Boundary Conditions ◽

Difference Equations ◽

Contraction Mapping ◽

Sufficient Conditions ◽

Degree Theory ◽

Integral Boundary Conditions ◽

Integral Boundary ◽

Krasnoselskii’S Fixed Point Theorem ◽

Quantum Numbers ◽

Derivatives Of

This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinearq-difference equations with three-pointq-integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach's contraction mapping, Krasnoselskii's fixed-point theorem, and Leray-Schauder degree theory, some new existence results are obtained. Two examples illustrate our results.

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Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions

Annales de l Institut Henri Poincaré Probabilités et Statistiques ◽

10.1214/10-aihp357 ◽

2011 ◽

Vol 47 (2) ◽

pp. 395-424 ◽

Cited By ~ 2

Author(s):

Mireille Bossy ◽

Mamadou Cissé ◽

Denis Talay

Keyword(s):

Boundary Conditions ◽

Variational Inequalities ◽

Neumann Boundary ◽

Neumann Boundary Conditions ◽

One Dimensional ◽

Stochastic Representations ◽

Derivatives Of

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A NEW KIND OF FUZZY RELATIONAL EQUATIONS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488510006568 ◽

2010 ◽

Vol 18 (03) ◽

pp. 333-342 ◽

Cited By ~ 1

Author(s):

FENG QIN ◽

PING FANG

Keyword(s):

Unique Solvability ◽

Complete Solution ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Solution Set ◽

Fuzzy Relational Equations ◽

Necessary And Sufficient

In this paper, a new kind of fuzzy relational equations (FREs for short) A ∘R*x = b is first introduced, and then the problem of solving solution to the FREs is discussed, where A is an m × n matrix, x and b are an n and an m dimensional column vectors, respectively. More specifically, their solvability and unique solvability are investigated, the corresponding necessary and sufficient conditions are presented, the complete solution set is obtained. It is worth noting the method to construct the complete solution set.

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CONVERGENCE IN RELAXATION SPECTRUM RECOVERY

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972716000861 ◽

2016 ◽

Vol 95 (1) ◽

pp. 121-132 ◽

Cited By ~ 1

Author(s):

R. J. LOY ◽

F. R. DE HOOG ◽

R. S. ANDERSSEN

Keyword(s):

Infinite Series ◽

Relaxation Spectrum ◽

Sufficient Conditions ◽

Convolution Equation ◽

Series Expansions ◽

Practical Application ◽

Rigorous Analysis ◽

Spectrum Recovery ◽

Derivatives Of

Because of its practical and theoretical importance in rheology, numerous algorithms have been proposed and utilised to solve the convolution equation $g(x)=(\text{sech}\,\star h)(x)\;(x\in \mathbb{R})$ for $h$, given $g$. There are several approaches involving the use of series expansions of derivatives of $g$, which are then truncated to a small number of terms for practical application. Such truncations can only be expected to be valid if the infinite series converge. In this note, we examine two specific truncations and provide a rigorous analysis to obtain sufficient conditions on $g$ (and equivalently on $h$) for the convergence of the series concerned.

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Connectedness of Solution Sets for Weak Vector Variational Inequalities on Unbounded Closed Convex Sets

Abstract and Applied Analysis ◽

10.1155/2013/431717 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5

Author(s):

Ren-you Zhong ◽

Yun-liang Wang ◽

Jiang-hua Fan

Keyword(s):

Variational Inequality ◽

Variational Inequalities ◽

Convex Sets ◽

Vector Variational Inequality ◽

Vector Variational Inequalities ◽

Solution Set ◽

Solution Sets ◽

Finite Dimensional ◽

Path Connectedness ◽

Weak Vector

We study the connectedness of solution set for set-valued weak vector variational inequality in unbounded closed convex subsets of finite dimensional spaces, when the mapping involved is scalarC-pseudomonotone. Moreover, the path connectedness of solution set for set-valued weak vector variational inequality is established, when the mapping involved is strictly scalarC-pseudomonotone. The results presented in this paper generalize some known results by Cheng (2001), Lee et al. (1998), and Lee and Bu (2005).

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