Fixed-Point Theory on a Frechet Topological Vector Space (original) (raw)

The Schauder and Krasnoselskii Fixed-Point Theorems on a Frechet Space

Mediterranean Journal of Mathematics, 2018

In this manuscript, we study some fixed-point theorems of the Schauder and Krasnoselskii type in a Frechet topological vector space E. We prove a fixed-point theorem which is for every weakly compact map from a closed bounded convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has a fixed point. Using our results, we will establish a new version of the Krasnoselskii fixed-point theorem.

Krasnoselskii's fixed point theorem for weakly continuous maps

2003

We consider the sum A + B : M → X , where M is a weakly compact and convex subset of a Banach space X , A : M → X is weakly continuous, and B ∈ L(X ) with B p 6 1, p ¿ 1. An alternative condition is given in order to guarantee the existence of ÿxed points in M for A + B. Some illustrative applications are given. ?

Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

Annales Mathematicae Silesianae, 2021

In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

Some fixed point theorems for nonconvex spaces

International Journal of Mathematics and Mathematical Sciences, 1998

We give a theorem for nonconvex topological vector spaces which yields the classical fixed point theorems of Ky Fan, Kim, Kaczynski, Kelly and Namioka as immediate consequences, and prove a new fixed point theorem for set-valued maps on arbitrary topological vector spaces.

An Extension of Tychonoff Fixed Point Theorem

2019

In this paper, we introduce the concepts of weaknorm, quasi-weaknorm on real vector spaces. By these concepts, we introduce the concept of quasi-locally convex topological vector spaces, which include locally convex topological vector spaces as special cases. By the Fan-KKM theorem, we prove a fixed point theorem in quasi-locally convex topological vector spaces, that is a natural extension of Tychonoff fixed point theorem in locally convex topological vector spaces. Then we provide an example to show that this extension is a proper extension.

The approximate fixed point property in Hausdorff topological vector spaces and applications

Discrete and Continuous Dynamical Systems, 2009

Let C be a compact convex subset of a Hausdorff topological vector space (E, τ ) and σ another Hausdorff vector topology in E. We establish an approximate fixed point result for sequentially continuous maps f : (C , σ) → (C , τ ). As application, we obtain the weakapproximate fixed point property for demicontinuous self-mapping weakly compact convex sets in general Banach spaces and use this to prove new results in asymptotic fixed point theory. These results are also applied to study the existence of limiting-weak solutions for differential equations in reflexive Banach spaces.

A fixed point theorem without convexity

2000

The purpose of this paper is to extend Himmelberg's fixed point theorem replacing the usual convexity in topological vector spaces by an abstract topological notion of convexity which generalizes classical convexity as well as several metric convexity structures found in the literature.

Fixed Point Theorems on Spaces Endowed with Vector-Valued Metrics

Fixed Point Theory and Applications, 2010

The purpose of this work is to present some local and global fixed point results for singlevalued and multivalued generalized contractions on spaces endowed with vector-valued metrics. The results are extensions of some theorems given by , and so forth.