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New fixed point theorems for set-valued contractions in b-metric spaces

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Abstract

In this paper, we indicate a way to generalize a series of fixed point results in the framework of b-metric spaces and we exemplify it by extending Nadler’s contraction principle for set-valued functions (see Nadler, Pac J Math 30:475–488, 1969) and a fixed point theorem for set-valued quasi-contraction functions due to Aydi et al. (see Fixed Point Theory Appl 2012:88, 2012).

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Acknowledgements

The authors are indebted to the anonymous referees for the careful and competent reading of the present paper and for their valuable suggestions.

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  1. Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014, Bucharest, Romania

    Radu Miculescu & Alexandru Mihail

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  1. Radu Miculescu
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  2. Alexandru Mihail
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Correspondence to Radu Miculescu.

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Miculescu, R., Mihail, A. New fixed point theorems for set-valued contractions in b-metric spaces. J. Fixed Point Theory Appl. 19, 2153–2163 (2017). https://doi.org/10.1007/s11784-016-0400-2

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