We establish the Leray–Schauder type theorems for very general classes of multifunctions, which are called admissible. Our admissible classes contain compositions of important multifunctions in nonlinear analysis and algebraic topology. Moreover, our arguments are elementary, without using the concept of degree of maps or theory of homotopy extensions. The Leray–Schauder principle [LS], one of ...

In this work we give a generalization of the results established by W. Ruckle and L. W. Baric for the matrix transformations which preserve schauder basis in the classical case for a p-adic analysis. We give several characterizations of matricial operators which preserve Schauder bases in non archimedean Barrelled spaces. Mathematics Subject Classification: 46A35

We give a direct proof for theorem 2 [13] (which is equivalent to theorem 1 [15]). Then we apply theorems 1 [15] and 4 [15] to some concrete spaces of sequences or functions which have a Schauder basis. The polynomials xj(t) = t j , j ∈ N considered in the classical moment problem, are replaced by the elements of the Schauder basis. Mathematics Subject Classification: 46A22, 47A57.

This paper provides a fixed point theorem à la Schauder, where the mappings considered are possibly discontinuous. Our main result generalizes and unifies several well-known results. Résumé: Nous prouvons dans cet article un théorème de point fixe du type Schauder (dont un corollaire en dimension finie est le théorème de Brouwer) pour des applications qui peuvent présenter des discontinuités. N...

Let X be a Banach space with an unconditional finite-dimensional Schauder decomposition (E n). We consider the general problem of characterizing conditions under which one can construct an unconditional basis for X by forming an unconditional basis for each E n. For example, we show that if sup dim E n < ∞ and X has Gordon-Lewis local unconditional structure then X has an unconditional basis of...

In this paper, we establish the existence of local and global mild solution for an impulsive fractional integro-differential equation with state dependent delay subject to nonlocal initial condition. The existence results for local mild solution are proved by applying the Schauder, nonlinear Larey Schauder alternative and Banach fixed point theorems. Then, we prove global existence result. An e...

Proof. Let g(x) = u(x) − sup∂Br(y) u − r2 − |x − y|2 2n supBr(y) f . We have ∆g = ∆u + supBr(y) f ≥ − f + supBr(y) f ≥ 0, that is, g is subharmonic in Br(y). Then supBr(y) g = sup∂Br(y) g = 0, so g ≤ 0 in Br(y) and the lemma follows. Lemma 2. If u is a solution to ∆u = f in Br(y) and v solves ∆v = 0 and v = u on ∂Br(y), then r2 − |x − y|2 2n inf Br(y) f ≤ v(x) − u(x) ≤ r 2 − |x − y|2 2n sup Br(...