In this paper, we introduce a new class of generalized nonlinear multivalued mixed quasi-variational-like inequalities and prove the existence and uniqueness of solutions for the class of generalized nonlinear multivalued mixed quasi-variational-like inequalities in reflexive Banach spaces using Fan-KKM Theorem.

The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E. Keywords—Common fixed point, Mann iteration, Multivalued mapping, weak convergence.

We investigate the convergence of measurable selectors for the limit of measurable multivalued maps. The relationship between the convergence of measurable selectors and lower and upper limits of measurable multivalued mappings with closed images is also derived. c © 2007 Elsevier Ltd. All rights reserved.

Abstract Multivalued $$*$$ ∗ -nonexpansive mappings are studied in Banach spaces. The demiclosedness principle is established. Here we focus on the problem of solving a variational inequality which defined set fixed points multivalued mapping. For this purpose, introduce tw...

and Applied Analysis 3 Remark 1.1. If E is a reflexive strictly convex and smooth Banach space, then for x, y ∈ E, φ x, y 0 if and only if x y. It is sufficient to show that if φ x, y 0 then x y. From 1.6 , we have ‖x‖ ‖y‖. This implies 〈x, Jy〉 ‖x‖2 ‖Jy‖2. From the definitions of j, we have Jx Jy, that is, x y, see 8, 9 for more details. Let C be a nonempty closed convex subset of a smooth Bana...

in this paper, we establish and prove the existence of best proximity points for multivalued cyclic $f$- contraction mappings in complete metric spaces. our results improve and extend various results in literature.

Functional dependencies [4] and multivalued dependencies [5,11] are important, widely-studied constraints on databases. A fundamental issue in database theory is the question of determining whether or not a given set of dependencies (in our case, functional and multivalued dependencies) logically implies another given dependency. We provide a simple and elegant set-theoretic characterization fo...

Recently, the issues of how to define functional dependencies (XFDs) and multivalued dependencies (XMVDs) in XML have been investigated. In this paper we consider the problem of checking the satisfaction of a set of XMVDs in an XML document. We present an algorithm using extensible hashing to check whether an XML document satisfies a given set of XMVDs. The performance of the algorithm is shown...