Throughout the sequel, E denotes a reflexive real Banach space and E∗ its topological dual. We also assume that E is locally uniformly convex. This means that for each x ∈ E, with ‖x‖ = 1, and each > 0, there exists δ > 0 such that, for every y ∈ E satisfying ‖y‖ = 1 and ‖x− y‖ ≥ , one has ‖x + y‖ ≤ 2(1 − δ). Recall that any reflexive Banach space admits an equivalent norm with which it is loca...

In this paper we prove Leray-Schauder and Furi-Pera types fixed point theorems for a class of multi-valued mappings with weakly sequentially closed graph. Our results improve and extend previous results for weakly sequentially closed maps and are very important in applications, mainly for the investigating of boundary value problems on noncompact intervals.

On Operators whose Compactness Properties are defined by Order by Safak Alpay Abstract. Let E be a Banach lattice. A subset B of E is called order bounded if there exist a, b in E such that a ≤ x ≤ b for each x ∈ B. Considering E in E′′, the bidual of E, a subset B of E is called b-order bounded in E if it is order bounded in the Banach lattice E′′. A bounded linear operator T : E → X is called...

A convex set C ⊆ X∗∗ × X∗ admits the variant Banach-Dieudonné property (VBDP) if the weak∗-strong closure C w×‖·‖ is the smallest set containing C that is closed to all limits of its bounded and weak∗×‖ · ‖ convergent nets. We show in particular, that all convex sets in X∗∗×X∗ admit the VBDP when E∗ := X∗×X∗∗ is weakly-compactly generated (WCG) and hence if E is either a dual separable or a ref...

ABSTRACT. With S a linearly ordered set with the least upper bound property, with g a nonincreasing real-valued function on S, and with A a densely denned dissipative linear operator, an evolution system M is developed to solve the modified Stieljes integral equation M(s, i)x = x + A((L)[sdgM(-, t)x). An affine version of this equation is also considered. Under the hypothesis that the evolufion...

Bridges 1992 has constructively shown the existence of continuous demand function for consumers with continuous, uniformly rotund preference relations. We extend this result to the case of multivalued demand correspondence. We consider a weakly uniformly rotund and monotonic preference relation and will show the existence of convex-valued demand correspondence with closed graph for consumers wi...

We prove that any Banach space X whose Banach-Mazur distance to a Hilbert space is less than √ 5+ √ 13 2 has the fixed point property for nonexpansive mappings. Let C be a nonempty closed convex subset of a Banach space X . A mapping T : C → C is said to be nonexpansive if ‖T x− T y‖ ≤ ‖x− y‖ for any x, y ∈ C. A nonempty weakly compact convex set C is said to have the fixed point property if ev...

In this paper we introduce intuitionistic fuzzy contra regular weakly generalized open mappings and intuitionistic fuzzy contra regular weakly generalized closed mappings. We investigate some of their properties.

A classical theorem due to R. Phelps states that if C is a weakly compact set in a Banach space E, the strongly exposing functionals form a dense subset of the dual space E. In this paper, we look at the concrete situation where C € L1pRdq is the closed convex hull of the set of random variables Y P L1pRdq having a given law ν. Using the theory of optimal transport, we show that every random va...