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On the Generalized Hyers–Ulam Stability of the Pexider Equation on Restricted Domains

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Handbook of Functional Equations

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 96))

Abstract

Let σ: \(E\longrightarrow E\) be an involution of the normed space E and let p, M, d be nonnegative real numbers, such that \(0<p<1\). In this chapter, we investigate the Hyers–Ulam–Rassias stability of the Pexider functional equations

$$\begin{aligned} f(x+y) = &\, g(x)+h(y),\ f(x+y)+g(x-y)=h(x)+k(y),\\ & f(x+y)+g(x+\sigma(y))=h(x)+k(y), x,y\in{E}\end{aligned}$$

on restricted domains \(\mathcal{B}=\{(x,y)\in{E^{2}}: \|x\|^{p}+\|y\|^{p}\geq M^{p}\}\) and \(\mathcal{C}=\{(x,y)\in{E}^{2}:\|x\|\geq d\; or\; \|y\|\geq d\}.\)

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Authors and Affiliations

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

    Youssef Manar

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

    Elhoucien Elqorachi

  3. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

    Themistocles M. Rassias

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  1. Youssef Manar
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  2. Elhoucien Elqorachi
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  3. Themistocles M. Rassias
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Correspondence to Youssef Manar .

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

    Themistocles M. Rassias

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Manar, Y., Elqorachi, E., Rassias, T. (2014). On the Generalized Hyers–Ulam Stability of the Pexider Equation on Restricted Domains. In: Rassias, T. (eds) Handbook of Functional Equations. Springer Optimization and Its Applications, vol 96. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1286-5_13

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