J. Fixed Point Theory Appl. 17 (2007) 1–32 DOI 10.1007/s11784-016-0289-9 © Springer International Publishing 2016 Journal of Fixed Point Theory and Applications Hybrid fixed point theorems for multivalued mappings in Banach algebras under a weak topology setting Afif Ben Amar, Mohamed Boumaiza and Donal O’Regan Abstract. In this paper, we introduce a new class of multivalued map- pings of the form I-C A , where A and C are multivalued mappings acting on Banach algebras. Using this concept, we present some fixed point the- orems 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 well- known results on the subject. An application to illustrate our theory is included. Mathematics Subject Classification. 47H04, 47H10. Keywords. Measures of weak noncompactness, multivalued mapping, weakly condensing, weakly sequentially closed graph, fixed point the- orem, integral inclusion. 1. Introduction In [12], Dhage presented some fixed point theorems in Banach algebras for the multivalued mapping AB, where A is Lipschitzian and B is compact, and he used these results to establish existence of solutions for differential inclusions. Recently, many authors examined the nonlinear operator equation x = AxBx + Cx (1.1) in Banach algebras using the measure of weak noncompactness (see [4, 6, 7, 8]). Since the product of two weakly convergent sequences is not necessarily weakly convergent, the authors in [6, 7] overcame this problem by looking at a class of Banach algebras satisfying a certain sequential condition (P ). The definition of the single-valued mapping I -C A and its invertibility play a fundamental role in the arguments. An extension of these results can be found in [8] where the single-valued mapping A is quasi-regular.