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Set-Valued Mapping and Rough Probability [PDF]
Mathematical Sciences Letters, 2018 In 1982, the theory of rough sets proposed by Pawlak and in 2013, Luay concerned a rough probability by using the notion of Topology. In this paper, we study the rough probability in the stochastic approximation spaces by using set-valued mapping and obtain results on rough expectation, and rough variance.
Sedghi, Shaban +3 more
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Set-Valued Robust Mappings and Approximatable Mappings
Journal of Mathematical Analysis and Applications, 1994 The second author recently proposed the concept of robustness of sets and functions for weakening the requirement of continuity of the objective functions and constraints in global optimization problems. In this paper the authors propose the concept of lower robustness and of lower approximation for a set-valued mapping and show that any lower ...
Shi, S.Z., Zheng, Q., Zhuang, D.M.
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The Tikhonov Regularization Method for Set-Valued Variational Inequalities
Abstract and Applied Analysis, 2012 This paper aims to establish the Tikhonov regularization theory for set-valued variational inequalities. For this purpose, we firstly prove a very general existence result for set-valued variational inequalities, provided that the mapping involved has ...
Yiran He
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Convergence of Inexact Iterative Schemes for Nonexpansive Set-Valued Mappings
Fixed Point Theory and Applications, 2010 Taking into account possibly inexact data, we study iterative schemes for approximating fixed points and attractors of contractive and nonexpansive set-valued mappings, respectively.
Simeon Reich, Alexander J. Zaslavski
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Continuous Selections for Set-Valued Mappings
Journal of Mathematical Analysis and Applications, 1994 It is proved that any almost lower semicontinuous multifunction (in the meaning of Deutsch and Kenderov) defined on a paracompact space and taking closed, convex, not necessarily bounded subsets of the real line as values, admits a continuous selector.
Lin, W.
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Generalization of Pawlak’s Approximations in Hypermodules by Set-Valued Homomorphisms
Foundations of Computing and Decision Sciences, 2017 The initiation and majority on rough sets for algebraic hyperstructures such as hypermodules over a hyperring have been concentrated on a congruence relation.
Mirvakili Saeed +2 more
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Convergence Results for Contractive Type Set-Valued Mappings
AxiomsIn this work, we study an iterative process induced by a contractive type set-valued mapping in a complete metric space and show its convergence, taking into account computational errors.
Alexander J. Zaslavski
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S-derivative of perturbed mapping and solution mapping for parametric vector equilibrium problems
Journal of Inequalities and Applications, 2021 In this paper, we deal with the sensitivity analysis in vector equilibrium problems by using the S-derivative of a set-valued mapping. We first investigate the S-derivative on a kind of set-valued gap function for the vector equilibrium problems.
Xicai Deng, Wei Zhao
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Stable approximations of set-valued maps [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 1988 The celebrated Lax’ principle “stability and consistency implies convergence” is adapted to the case of nonlinear equation and even inclusions (multivalued equations) through a convenient concept of stability. It requires the definition of “contingent derivative” of single or set-valued maps and states that a family of maps is stable if and only if the
Aubin, J.-P., Wets, R.J.-B.
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Some Maximal Elements' Theorems in FC-Spaces
Journal of Inequalities and Applications, 2009 Let I be a finite or infinite index set, let X be a topological space, and let (Yi,φNi)i∈I be a family of FC-spaces. For each i∈I, let Ai:X→2Yi be a set-valued mapping. Some new existence theorems of maximal elements for a set-
Rong-Hua He, Yong Zhang
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