Asymptotic stability in 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

Stability and Asymptotic Fixed-point Theory.

Ulam - Hyers Stability Theorem by Tripled Fixed Point Theorem

This paper deals with tripled fixed point theorem, and the approach is based on Perov-type fixed point theorem for contractions in metric spaces endowed with vector-valued metrics. We are also study Ulam-Hyers stability results for the tripled fixed points of a triple of contractive type single-valued and respectively multi-valued operators on complete metric spaces.

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.