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A fixed point theorem for positive strict set-contractions mappings and its application to Urysohn type integral equations

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Abstract

Inspired by the work in Dix and Karakostas (Nonlinear Anal. 71:3872–3880, 2009), we prove in this paper a new fixed point theorem for strict-set contractions leaving invariant a cone in a Banach space. This new result is used to obtain an existence result for Urysohn type integral equations.

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Authors and Affiliations

  1. Faculty of Mathematics, USTHB, Po. Box 32, El-Alia, Bab-ezouar, Algiers, Algeria

    Abdelhamid Benmezaï

  2. EPSTA, Po. Box 474, Place des Martyrs, Algiers, Algeria

    Besma Boucheneb

Authors
  1. Abdelhamid Benmezaï
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  2. Besma Boucheneb
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Correspondence to Abdelhamid Benmezaï.

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Benmezaï, A., Boucheneb, B. A fixed point theorem for positive strict set-contractions mappings and its application to Urysohn type integral equations. Arch. Math. 105, 389–399 (2015). https://doi.org/10.1007/s00013-015-0802-1

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  • DOI: https://doi.org/10.1007/s00013-015-0802-1

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