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Common fixed point theorem for cyclic generalized multi-valued contraction mappings. (English) Zbl 1254.54065
Authors’ abstract: We extend a multi-valued contraction mapping to a cyclic multi-valued contraction mapping. We also establish the existence of a common fixed point theorem for a cyclic multi-valued contraction mapping. Our results extend, generalize and unify Nadler’s multi-valued contraction mappings and many fixed point theorems for multi-valued mappings.
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H04Set-valued operators
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