The best approximation problem in a hyperconvex metric space consists of finding conditions for given set-valued mappings F andG and a setX such that there is a point x0 ∈ X satisfying d G x0 , F x0 ≤ d x, F x0 for x ∈ X. When G I, the identity mapping, and when the set X is compact, best approximation theorems for mappings in hyperconvex metric spaces are given for the single-valued case in 1–...

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, letAi : X → 2i be a set-valued mapping. Some new existence theorems of maximal elements for a set-valued mapping and a family of set-valued mappings involving a better admissible set-valuedmapping are established under noncompact setting of FC-spaces. Our results ...

Abstract In this paper, we study a first-order solution method for particular class of set optimization problems where the concept is given by approach. We consider case in which set-valued objective mapping identified finite number continuously differentiable selections. The corresponding problem then equivalent to find optimistic solutions vector under uncertainty with set. develop optimality...

The purpose of this paper is to study common fixed point theorems for six (four single-valued and two set-valued) mappings in fuzzy metric spaces. without assuming compatibility and continuity of any mapping on non complete metric spaces. To prove the theorem, we use a non compatible condition, that is, weak commutativity of type (Kh)in fuzzy metric spaces. We show that completeness of the whol...

Unlike monotone single-valued functions, multi-valued mappings may have none, one or (possibly infinitely) many minimal fixed-points. The contribution of this work is twofold. At first we overview and investigate about the existence and computation of minimal fixed-points of multi-valued mappings, whose domain is a complete lattice and whose range is its power set. Second, we show how these res...

Abstract This paper presents two fixed point results for both single valued and multivalued mappings on F -metric spaces, which is introduced by Jleli Samet [1]. First, we consider the concept of P -contraction mappings. Then using Feng-Liu’s technique, present a result -closed set spaces.

For upper semicontinuous finite-dimensional set-valued mappings with either convex closed or aspheric closed values we prove the existence of special continuous e -approximations that point-wise converge to a Borel measurable selector of the set-valued mapping as e tends to zero. For convex-valued case the convergence holds on the entire domain while for aspheric-valued case — on a certain coun...

In this paper, using proximal-point mappings technique of Raccretive mappings and the property of the fixed point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of the system of parametric generalized quasi-variational inclusions involving R-accretive mappings in real uniformly smooth Banach space. Further under suitable conditions, we...