FIXED POINTS AND SOLUTIONS OF OPERATOR EQUATIONS FOR THE WEAK TOPOLOGY IN BANACH ALGEBRAS

In this paper we prove some fixed point theorems for operators acting in Banach algebras and satisfying conditions expressed mainly with help of weak topology and measures of weak noncompactness. The existence of solutions to some class of operator equations in Banach algebras is also discussed. Som...

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Published inTaiwanese journal of mathematics Vol. 18; no. 3; pp. 871 - 893
Main Authors Banaś, Józef, Taoudi, Mohamed-Aziz
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.06.2014
Subjects
Algebra
Algebraic topology
Banach space
Diagonal lemma
Differential equations
Mathematical theorems
Mathematics
Perceptron convergence procedure
Topological compactness
Topological theorems
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ISSN1027-5487
2224-6851
DOI10.11650/tjm.18.2014.3860

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Summary:In this paper we prove some fixed point theorems for operators acting in Banach algebras and satisfying conditions expressed mainly with help of weak topology and measures of weak noncompactness. The existence of solutions to some class of operator equations in Banach algebras is also discussed. Some examples are presented to illustrate our results. 2010Mathematics Subject Classification: 47H08, 47H09. Key words and phrases: Banach algebra, Weakly compact set, Weakly sequentially continuous operator, Measure of weak noncompactness, Fixed point theorem, Operator equation, Dunford-Pettis property.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.18.2014.3860