Hybrid fixed point theorems for multivalued mappings in Banach algebras under a weak topology setting |
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| Authors: | Afif Ben Amar Mohamed Boumaiza Donal O’Regan |
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| Affiliation: | 1.Department of Mathematics, Faculty of Sciences,Sfax University,Sfax,Tunisia;2.Higher School of Sciences and Technologies of Hammam Sousse,Hammam Sousse,Tunisia;3.School of Mathematics, Statistics and Applied Mathematics,National University of Ireland,Galway,Ireland;4.Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics,King Abdulaziz University,Jeddah,Saudi Arabia |
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| Abstract: | In this paper, we introduce a new class of multivalued mappings of the form ({frac{I-C}{A}}), where ({A}) and ({C}) are multivalued mappings acting on Banach algebras. Using this concept, we present some fixed point theorems in Banach algebras satisfying a certain sequential condition (({P})) in the weak topology setting. Our main tool is the axiomatic measure of weak noncompactness. Our results generalize, extend and improve wellknown results on the subject. An application to illustrate our theory is included. |
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