THE LERAY-SCHAUDER CONDITION FOR 1-SET WEAKLY-CONTRACTIVE AND (ws)-COMPACT OPERATORS

doi:10.1016/S0252-9602(14)60003-5

Abstract

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.

Key words: Measure of weak noncompactness, weakly condensing and weakly nonexpan-sive, (ws)-compact operator, fixed point theorems, semi-closed at the origin

CLC Number:

47H10

Afif BEN AMAR. THE LERAY-SCHAUDER CONDITION FOR 1-SET WEAKLY-CONTRACTIVE AND (ws)-COMPACT OPERATORS[J].Acta mathematica scientia,Series B, 2014, 34(2): 263-273.

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