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.