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

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.