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Generalized Meir-Keeler type contractions and discontinuity at fixed point. (English) Zbl 1460.54038

Summary: In this paper, we show that generalized Meir-Keeler type contractive definitions are strong enough to generate a fixed point but do not force the mapping to be continuous at the fixed point. Thus we provide more answers to the open question posed by B. E. Rhoades [Contemp. Math. 72, 233–245 (1988; Zbl 0649.54024)].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54E50 Complete metric spaces

Citations:

Zbl 0649.54024
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Full Text: DOI

References:

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