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HYBRID-TYPE OF FIXED-SET RESULTS IN BANACH ALGEBRAS INVOLVING THE SUM AND THE PRODUCT OF MULTI-VALUED MAPPINGS UNDER WEAK TOPOLOGY
  • KHaled Ben Amara,
  • Aref JERIBI,
  • najib Kaddachi
KHaled Ben Amara
University of Sfax Faculty of Sciences of Sfax
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Aref JERIBI
University of Sfax Faculty of Sciences of Sfax
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najib Kaddachi
University of Sfax Faculty of Sciences of Sfax
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Abstract

In this manuscript, by means of the technique of measures of weak noncompactness, we prove some fixed set results for the sum and the product of (p+1) multi-valued mappings Pp i=1 A Bi; acting on Banach algebras satisfying a certain sequential condition (P) under weak topology. In addition, by using a new definition of the multi-valued mapping I A ; we get new fixed set theorems for the mappings of the form I A 1 Pni =1 Bi under some suitable conditions on the operators A; B1; : : : ; Bp in Banach algebras. Applications to the theory of self-similarity are also given.