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Fixed-point theorems for multivalued operator matrix under weak topology with an application. (English) Zbl 1503.47077

Summary: 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.

MSC:

47H10 Fixed-point theorems
47H04 Set-valued operators
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
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