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A generalization of set-valued Prešić–Reich type contractions in ultrametric spaces with applications

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Abstract

In this paper, we study the existence and uniqueness of coincidence and common fixed point of a set-valued and a single-valued mapping satisfying generalized set-valued Prešić–Reich type contractive condition in ultrametric spaces without the property of completeness. As an application, the well-posedness of a common fixed point problem is proved. An example is given to illustrate our results. Our results generalize and extend the results of Prešić–Reich in the context of ultrametric spaces.

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Authors and Affiliations

  1. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai, Tamil Nadu,  600 005, India

    D. Ramesh Kumar & M. Pitchaimani

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  1. D. Ramesh Kumar
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  2. M. Pitchaimani
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Correspondence to D. Ramesh Kumar.

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Kumar, D.R., Pitchaimani, M. A generalization of set-valued Prešić–Reich type contractions in ultrametric spaces with applications. J. Fixed Point Theory Appl. 19, 1871–1887 (2017). https://doi.org/10.1007/s11784-016-0338-4

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