HYBRID-TYPE OF FIXED-SET RESULTS IN BANACH ALGEBRAS INVOLVING THE SUM
AND THE PRODUCT OF MULTI-VALUED MAPPINGS UNDER WEAK TOPOLOGY
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.