A remark to the Schauder fixed point theorem

A Remark to the Schauder Fixed Point Theorem

In the paper some sufficient conditions are established in order that a continuous map have a fixed point. The results are related to those obtained by R. D. Nussbaum in [18], L. Górniewicz and D. RozpłochNowakowska in [12], S. Szufla in [21] and D. Bugajewski in [6]. The famous Schauder Fixed Point Theorem [20] has been generalized in various directions by using different methods. For referenc...

Schauder Fixed Point Theorem in Spaces with Global Nonpositive Curvature

Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order

In this paper, by using Schauder fixed point theorem, we study the existence of at least one positive solution to a coupled system of fractional boundary value problems given by { −D1 0+ y1(t) = λ1a1(t)f(t, y1(t), y2(t)) + e1(t), −D2 0+ y2(t) = λ2a2(t)g(t, y1(t), y2(t)) + e2(t), where ν1, ν2 ∈ (n− 1, n] for n > 3 and n ∈ N , subject to the boundary conditions y 1 (0) = 0 = y (i) 2 (0), for 0 ≤ ...

A generalization of the Schauder fixed point theorem via multivalued contractions

We establish a fixed point theorem for a continuous function f : X → E, where E is a Banach space and X ⊆ E. Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.

Vector ultrametric spaces and a fixed point theorem for correspondences

In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.