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The Leray-Schauder condition for 1-set weakly-contractive and (ws)-compact operators

Authors
  • BEN AMAR, Afif1
  • 1 Department of Mathematics
Type
Published Article
Journal
Acta Mathematica Scientia
Publication Date
Jan 01, 2014
Volume
34
Issue
2
Pages
263–273
Identifiers
DOI: 10.1016/S0252-9602(14)60003-5
Source
Elsevier
Keywords
License
Unknown

Abstract

The main purpose of this article is to prove a collection of new fixed point theorems for (ws)-compact and so-called 1-set weakly contractive operators under Leray-Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for (ws)-compact (in particular nonexpansive) self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations.

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