## 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:

 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 54E40 Special maps on metric spaces
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### References:

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