Hybrid fixed point theorems for multivalued mappings in Banach algebras under a weak topology setting

Afif Ben Amar; Mohamed Boumaiza; Donal O’Regan

doi:10.1007/s11784-016-0289-9

Hybrid fixed point theorems for multivalued mappings in Banach algebras under a weak topology setting

Afif Ben Amar
, Mohamed Boumaiza
, Donal O’Regan

Mathematics

Mathematics University of Sfax
Higher School of Sciences and Technologies of Hammam Sousse
King Abdulaziz University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

18 Citations (Scopus)

Abstract

In this paper, we introduce a new class of multivalued mappings of the form I-CA, 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.

Original language	English
Pages (from-to)	327-350
Number of pages	24
Journal	Journal of Fixed Point Theory and Applications
Volume	18
Issue number	2
DOIs	https://doi.org/10.1007/s11784-016-0289-9
Publication status	Published - 1 Jun 2016

Keywords

Measures of weak noncompactness
fixed point theorem
integral inclusion
multivalued mapping
weakly condensing
weakly sequentially closed graph

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10.1007/s11784-016-0289-9

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abstract = "In this paper, we introduce a new class of multivalued mappings of the form I-CA, 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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AU - Ben Amar, Afif

AU - Boumaiza, Mohamed

AU - O’Regan, Donal

PY - 2016/6/1

Y1 - 2016/6/1

N2 - In this paper, we introduce a new class of multivalued mappings of the form I-CA, 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.

AB - In this paper, we introduce a new class of multivalued mappings of the form I-CA, 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.

KW - Measures of weak noncompactness

KW - fixed point theorem

KW - integral inclusion

KW - multivalued mapping

KW - weakly condensing

KW - weakly sequentially closed graph

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DO - 10.1007/s11784-016-0289-9

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EP - 350

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

IS - 2

ER -

Hybrid fixed point theorems for multivalued mappings in Banach algebras under a weak topology setting

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Keywords

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