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Weak reciprocal continuity and fixed point theorems. (English) Zbl 1223.54068
Authors’ abstract: The aim of the present paper is to introduce the notion of weak reciprocal continuity and obtain fixed point theorems by employing the new notion. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. Our results generalize several fixed point theorems.
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
54E40Special maps on metric spaces
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