where here, and in what follows, Eε denotes the expectation with respect to uniformly chosen ε = (ε1, . . . , εn) ∈ {−1, 1}. The infimum over all constants T for which (1.1) holds is denoted by Tp(X). An important theorem of Ribe [12] states that Banach spaces which are uniformly homeomorphic must have the same isomorphic local properties. In other words, any property which remains valid under ...

We study the asymptotic behavior of the sequence of the iterates for a nonexpansive mapping, defined on a suitable subset of a Banach space with Opial's condition. Some results are stated also for semigroups of nonexpansive mappings and for mappings of asymptotically nonexpansive type in uniformly convex Banach spaces with Opial's condition.

The purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in Banach spaces. Our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).

The Leray–Schauder degree is defined for mappings of the form I−C, where C is a compact mapping from the closure of an open bounded subset of a Banach space X into X. Since the fifties, a lot of work has been devoted in extending this theory to the same type of mappings on some nonlinear spaces, and in extending the class of mappings in the frame of Banach spaces or manifolds. New applications ...

The problem of controllability of linear and nonlinear systems represented by ordinary differential equations in finite dimensional spaces has been extensively studied. Several authors [5,6,12-14] have extended the concept to infinite dimensional systems in Banach spaces with bounded operators. Triggiani [17] established sufficient conditions for controllability of linear and nonlinear systems ...