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Fixed Points and Stability for Functional Equations in Probabilistic Metric and Random Normed Spaces

Fixed Point Theory and Applications volume 2009, Article number: 589143 (2009) Cite this article

Abstract

We prove a general Ulam-Hyers stability theorem for a nonlinear equation in probabilistic metric spaces, which is then used to obtain stability properties for different kinds of functional equations (linear functional equations, generalized equation of the square root, spiral generalized gamma equations) in random normed spaces. As direct and natural consequences of our results, we obtain general stability properties for the corresponding functional equations in (deterministic) metric and normed spaces.

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Authors and Affiliations

  1. Department of Mathematics, "Politehnica" University of Timişoara, Piaţa Victoriei number 2, 300006, Timişoara, Romania

    Liviu Cădariu

  2. Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, Vasile Pârvan 4, 300223, Timişoara, Romania

    Viorel Radu

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  1. Liviu Cădariu
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  2. Viorel Radu
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Correspondence to Liviu Cădariu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Cădariu, L., Radu, V. Fixed Points and Stability for Functional Equations in Probabilistic Metric and Random Normed Spaces. Fixed Point Theory Appl 2009, 589143 (2009). https://doi.org/10.1155/2009/589143

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  • DOI: https://doi.org/10.1155/2009/589143

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