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Some Integral Type Fixed-Point Theorems and an Application to Systems of Functional Equations

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Abstract

In this paper, we prove a new common fixed point theorem for four self mappings by using the notions of compatibility and subsequential continuity (alternate subcompatibility and reciprocal continuity) in metric spaces satisfying a general contractive condition of integral type. We give some examples to support the useability of our main result. Also, we obtain some fixed point theorems of Gregus type for four mappings satisfying a strict general contractive condition of integral type in metric spaces. We conclude the paper with an application of our main result to solvability of systems of functional equations.

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Acknowledgements

The authors would like to thank Professor Naseer Shahzad for a reprint of the paper [36]. The authors are grateful to the referees for their useful comments to improve the paper.

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Authors and Affiliations

  1. R.H. Government Postgraduate College, Kashipur, 244713, (U.S. Nagar), Uttarakhand, India

    Sunny Chauhan

  2. Institut Supérieur d’Informatique et des Technologies de Communication de Hammam Sousse, Université de Sousse, Route GP1-4011, H. Sousse, Tunisie

    Hassen Aydi

  3. Department of Mathematics, Hashemite University, P.O. Box 150459, Zarqa, 13115, Jordan

    Wasfi Shatanawi

  4. Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, via Archirafi 34, 90123, Palermo, Italy

    Calogero Vetro

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  1. Sunny Chauhan
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  2. Hassen Aydi
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Correspondence to Sunny Chauhan.

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Chauhan, S., Aydi, H., Shatanawi, W. et al. Some Integral Type Fixed-Point Theorems and an Application to Systems of Functional Equations. Viet J Math 42, 17–37 (2014). https://doi.org/10.1007/s10013-013-0030-6

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