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Hyers–Ulam–Rassias Stability of the Generalized Wilson’s Functional Equation

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Mathematical Analysis, Approximation Theory and Their Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 111))

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Abstract

In this chapter, we apply the fixed point theorem and the direct method to the proof of Hyers–Ulam–Rassias stability property for generalized Wilson’s functional equation

$$\displaystyle\begin{array}{rcl} \int _{K}\int _{G}f(xtk.y)dkd\mu (t) = f(x)g(y),\;x,y \in G,& & {}\\ \end{array}$$

where f, g are continuous complex valued functions on a locally compact group G, K is a compact subgroup of morphisms of G, dk is the normalized Haar measure on K and μ is a K-invariant complex measure with compact support.

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Author information

Authors and Affiliations

  1. Faculty of Sciences, Department of Mathematics, Ibn Zohr University, Agadir, Morocco

    Elqorachi Elhoucien

  2. Superior School of Technology, Ibn Zohr University, Guelmim, Morocco

    Youssef Manar

  3. Faculty of Sciences, Department of Mathematics, Ibn Tofail University, Kenitra, Morocco

    Sammad Khalil

Authors
  1. Elqorachi Elhoucien
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  2. Youssef Manar
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  3. Sammad Khalil
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Corresponding author

Correspondence to Elqorachi Elhoucien .

Editor information

Editors and Affiliations

  1. Department of Mathematics, National Technical Unversity of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Department of Mathematics, Netaji Subhas Instit. of Tech., New Delhi, India

    Vijay Gupta

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Elhoucien, E., Manar, Y., Khalil, S. (2016). Hyers–Ulam–Rassias Stability of the Generalized Wilson’s Functional Equation. In: Rassias, T., Gupta, V. (eds) Mathematical Analysis, Approximation Theory and Their Applications. Springer Optimization and Its Applications, vol 111. Springer, Cham. https://doi.org/10.1007/978-3-319-31281-1_9

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