Throughout this paper, let Z, E, and F be topological vector spaces, let X ⊆ E and Y ⊆ F be nonempty, closed, and convex subsets. Let D : X → 2X , T : X → 2Y and Ψ : X ×Y × X → 2Z be set-valued mappings, and let C : X → 2Z be a set-valued mapping such that C(x) is a closed pointed and convex cone with intC(x) = ∅ for each x ∈ X , where intC(x) denotes the interior of the set C(x). Then the gene...

In the present paper we establish an abstract principle of condensation of singularities for families consisting of set-valued mappings. By using it as a basic tool, the condensation of the singularities and the equicontinuity of certain families of generalized convex set-valued mappings are studied. In particular, a principle of condensation of the singularities of families of closed convex pr...

A new class of generalized nonlinear set-valued quasivariational inclusions involving generalizedm-accretive mappings in Banach spaces are studied, which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized m-accretive mappings, we established the equivalence between the generalized nonlinear set-va...

In this paper, a new system of nonlinear set-valued variational inclusions involving (H, η)-monotone mappings in Hilbert spaces is introduced and studied. By using the resolvent operator method associated with (H, η)-monotone mappings, an existence theorem of solutions for this kind of system of nonlinear set-valued variational inclusion is established and a new iterative algorithm is suggested...

The aim of this paper is to introduce the concept of intimate mappings in Complex valued metric space and prove a lemma and a common fixed point theorem for four mappings and provide examples in support of main theorem.

Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variati01~al analysis and its applications, especially for issues related to variational stability and optimizatiou. \Ve develop an approach to variational stability based on generalized differentiation. The principal achievements of this paper include new results on coderivative ...

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...

In this paper, we extend a multi-valued contraction mapping to a cyclic multi-valued contraction mapping. We also establish the existence of common fixed point theorem for a cyclic multi-valued contraction mapping. Our results extend, generalize and unify Nadler’s multi-valued contraction mapping and many fixed point theorems for multivalued mappings. © 2012 Elsevier Ltd. All rights reserved.

In this paper we define g-nonexpansive and g-nonexpansive type fuzzy mappings and prove common fixed point theorems for sequences of fuzzy mappings satisfying certain conditions on a Banach space. Thus we obtain fixed point theorems for nonexpansive type multi-valued mappings.