MEASURES OF WEAK NON COMPACTNESS, NONLINEAR LERAY-SCHAUDER ALTERNATIVES IN BANACH ALGEBRAS SATISFYING CONDITION (P) AND AN APPLICATION

被引：1

作者：

Ali, Amro Alsheikh ^{[1
]}

Ben Amar, Afif ^{[1
]}

机构：

[1] Sfax Univ, Fac Sci, Dept Math, LA 1171, Sfax 3000, Tunisia

来源：

QUAESTIONES MATHEMATICAE | 2016年 / 39卷 / 03期

关键词：

Measures of weak noncompactness; weakly condensing; weakly sequentially continuous; fixed point theorems; integral equation; OPERATORS; NONCOMPACTNESS;

D O I：

10.2989/16073606.2015.1070378

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Tu this paper, we establish some new nonlinear Leray-Schauder alternatives for the Sum and the product of weakly sequentially continuous operators in Banach algebras satisfying certain sequential condition (P). The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. As an application, our results are used to prove the existence of solutions for a nonlinear integral equation.

引用

页码：319 / 340

页数：22

共 6 条

[1] LERAY-SCHAUDER ALTERNATIVES FOR MAPS SATISFYING COUNTABLE COMPACTNESS CONDITIONS
O'Regan, Donal
[J]. ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2019, 27 (03): : 195 - 205
[2] Monch type Leray-Schauder alternatives for maps satisfying weakly countable compactness conditions
O'Regan, Donal
[J]. JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2019, 19 (01): : 29 - 34
[3] Nonlinear Alternatives of Leray-Schauder Type in Banach Algebra Involving Four Operators with Application
Jeribi, Aref
Moalla, Rihab
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2013, 34 (10) : 1097 - 1114
[4] Nonlinear Leray-Schauder alternatives and application to nonlinear problem arising in the theory of growing cell population
Ben Amar, Afif
[J]. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2011, 9 (04): : 851 - 865
[5] MEASURES OF WEAK NONCOMPACTNESS AND FIXED POINT THEORY IN BANACH ALGEBRAS SATISFYING CONDITION (P)
Ben Amar, Afif
O'Regan, Donal
[J]. FIXED POINT THEORY, 2017, 18 (01): : 37 - 46
[6] Nonlinear Leray-Schauder Alternatives for Decomposable Operators in Dunford-Pettis Spaces and Application to Nonlinear Eigenvalue Problems
Ben Amar, Afif
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2010, 31 (11) : 1213 - 1220

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