The main aim of this paper is twofold. Our first objective to study a new system generalized multivalued variational-like inequalities in Banach spaces and establish its equivalence with fixed point problems utilizing the concept P-?-proximal mapping. obtained alternative equivalent formulation used iterative algorithm for finding approximate solution suggested. Under some appropriate assumptio...

Let X be either a uniformly convex Banach space or a reflexive Banach space having the Opial property. It is shown that a multivalued nonexpansive mapping on a bounded closed convex subset of X has an endpoint if and only if it has the approximate endpoint property. This is the first result regarding the existence of endpoints for such kind of mappings even in Hilbert spaces. The related result...

Let (Ω,Σ) be a measurable space, with Σ a sigma-algebra of subset of Ω, and let C be a nonempty bounded closed convex separable subset of a Banach space X , whose characteristic of noncompact convexity is less than 1, KC(X) the family of all compact convex subsets of X . We prove that a multivalued nonexpansive non-self-random operator T :Ω×C → KC(X), 1-χ-contractive mapping, satisfying an inwa...

We introduce and study a new class of nonlinear general A-monotone operator equations with multivalued operator. By using Alber’s inequalities, Nalder’s results, and the new proximal mapping technique, we construct some new perturbed iterative algorithms with mixed errors for solving the nonlinear general A-monotone operator equations and study the approximationsolvability of the nonlinear oper...

In the present work, we introduce a new hybrid iterative process which is combination of proximal point algorithms and modified Krasnoselskii-Mann algorithm for approximating common element set minimizers convex function fixed points finite family multivalued strictly pseudo-contractive mappings in framework Hilbert spaces. We then prove strong convergence proposed without imposing any compactn...

The study of set differential equations has been initiated as an independent subject and several results of interest can be found in [4–5, 10–12, 14]. The interesting feature of the set differential equations is that the results obtained in this new framework become the corresponding results of ordinary differential equations as the Hukuhara derivative and the integral used in formulating the s...

and Applied Analysis 3 where R is the set of all real numbers; in particular, J(−x) = −J(x) for all x ∈ E ([28]). We say that a Banach space E has a weakly sequentially continuous duality mapping if there exists a gauge function φ such that the duality mapping Jφ is single valued and continuous from the weak topology to the weak topology; that is, for any {xn} ∈ E with xn ⇀ x, Jφ(xn) ∗ ⇀ Jφ(x)....

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.

We consider the case in which the available knowledge does not allow to specify a precise probabilistic model for the prior and/or likelihood in statistical estimation. We assume that this imprecision can be represented by belief functions models. Thus, we exploit the mathematical structure of belief functions and their equivalent representation in terms of closed convex sets of probabilities t...