| THE LERAY-SCHAUDER CONDITION FOR 1-SET WEAKLY-CONTRACTIVE AND （ws）-COMPACT OPERATORS |
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| 作者姓名： | Afif BEN AMAR |
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| 作者单位： | Department of Mathematics, Faculty of Sciences, Sfax, LA 1171, 3000, Tunisia |
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| 摘 要： | Abstract The main purpose of this article is to prove a collection of new nxea 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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| 关 键 词： | Hammerstein型积分方程 收缩 紧算子 Banach空间 不动点定理 边界条件 应用程序 运营商 |
THE LERAY-SCHAUDER CONDITION FOR 1-SET WEAKLY-CONTRACTIVE AND （ws）-COMPACT OPERATORS |
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| Afif BEN,AMAR.THE LERAY-SCHAUDER CONDITION FOR 1-SET WEAKLY-CONTRACTIVE AND （ws）-COMPACT OPERATORS[J].Acta Mathematica Scientia,2014(2):263-273. |
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| Authors: | 《Acta Mathematica Scientia》 |
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| 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 LeraySchauder 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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| Keywords: | Measure of weak noncompactness weakly condensing and weakly nonexpan-sire （ws）-compact operator fixed point theorems semi-closed at the origin |
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