Fixed-Point Theorems for Multivalued Operator Matrix Under Weak Topology with an Application

Abstract

In the present paper, we establish some fixed-point theorems for a $$2\times 2$$ block operator matrix involving multivalued maps acting on Banach spaces. These results are formulated in terms of weak sequential continuity and the technique of measures of weak noncompactness. The results obtained are then applied to a coupled system of nonlinear equations.