In this paper, we prove some approximate fixed point results for proximinal valued $beta$-contractive multifunctions on metric spaces. We show that our results generalize some old fixed point results in the literature.

The main result of the paper contains an exact formula for the rate of regularity of a set-valued mapping with a convex graph. As a consequence we find an exact expression for the rate of regularity of a set-valued mapping associated with so called constraint system. It turns out that the rate is equal to the upper bound of Robinson-type estimates over all norms in the graph space of the homoge...

Extremality, stationarity and regularity notions for a system of closed sets in a normed linear space are investigated. The equivalence of different abstract “extremal” settings in terms of set systems and multifunctions is proved. The dual necessary and sufficient conditions of weak stationarity (the Extended extremal principle) are presented for the case of an Asplund space.

Generalized and unified versions of coincidence or maximal element theorems of Fan, Yannelis and Prabhakar, Ha, Sessa, Tarafdar, Rim and Kim, Mehta and Sessa, Kim and Tan are obtained. Our arguments are based on our recent works on a broad class of multifunctions containing composites of acyclic maps defined on convex subsets of Hausdorff topological vector spaces.

In this paper we shall establish a result concerning the covering dimension of a set of the type {x ∈ X : Φ(x)∩Ψ(x) 6= ∅}, where Φ, Ψ are two multifunctions from X into Y and X, Y are real Banach spaces. Moreover, some applications to the differential inclusions will be given.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 19 January 2021Accepted: 07 September 2021Published online: 14 December 2021Keywordsstochastic programming, generalized differentiation, integral multifunctions, Liebniz rules, Lipschitzian stabilityAMS Subject Headings49J53, 90C15, 90C34, 49J52Publication DataISSN (print...

We introduce the spaces M Y,φ, M o,n Y,φ , M̃ Y,φ and M o Y,d,φ of multifunctions. We prove that the spaces M Y,φ and M Y,d,φ are complete. Also, we get some convergence theorems.

This paper is concerned with solvability and solution stability of parametric generalized equations governed by set-valued mappings. By a degree-theoretic approach for multifunctions, some new results on lower semicontinuity of the solution map to a parametric generalized equation are established.

We consider a Cauchy problem for a fractional semilinear differential inclusions involving Caputo’s fractional derivative in non separable Banach spaces under Filippov type assumptions and we prove the existence of solutions. MSC: 34A60, 26A33, 34B15 keywords: fractional derivative, fractional semilinear differential inclusion, Lusin measurable multifunctions.

in this paper, we prove some approximate fixed point results for proximinal valued $beta$-contractive multifunctions on metric spaces. we show that our results generalize some old fixed point results in the literature.