Abstract
In this paper we present some fixed point results for the sum of two mappings where S is a strict contraction and T is not necessarily weakly compact and satisfies a new condition formulated in terms of an axiomatic measure of weak noncompactness. Our fixed point results extend and improve several earlier results in the literature. In particular, our results encompass the analogues of Krasnosel’skii’s and Sadovskii’s fixed point theorems for sequentially weakly continuous mappings and a number of their generalizations. Finally, an application to integral equations is given to illustrate the usability of the obtained results. MSC:37C25, 40D05, 31B10.
Highlights
In, Schauder proved that every continuous and compact mapping from a nonempty closed convex subset of a Banach space to itself has a fixed point
Stimulated by some real world applications, we introduce the concept of power-convex condensing pair of sequentially weakly continuous mappings
We prove some fixed point theorems for the sum S + T where S is a strict contraction while T is power-convex condensing w.r.t
Summary
Krasnosel’skii-type fixed point theorems with applications to Volterra integral equations. Nawab Hussain1* and Mohamed Aziz Taoudi[2,3] Dedicated to Professor Wataru Takahashi on the occasion of his seventieth birthday
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