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  • Research Article
  • Open Access

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

Fixed Point Theory and Applications20092009:589143

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

  • Received: 24 April 2009
  • Accepted: 19 October 2009
  • Published:

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.

Keywords

  • Functional Equation
  • Nonlinear Equation
  • Generalize Equation
  • Differential Geometry
  • Normed Space

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Authors’ Affiliations

(1)
Department of Mathematics, "Politehnica" University of Timişoara, Piaţa Victoriei number 2, 300006 Timişoara, Romania
(2)
Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, Vasile Pârvan 4, 300223 Timişoara, Romania

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