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Solution and approximation of radical quintic functional equation related to quintic mapping in quasi-\(\beta \)-Banach spaces

  • Iz-iddine EL-Fassi
Original Paper

Abstract

Let \(\mathbb {R}\) denote the set of real numbers. The purpose of the present paper is first to introduce and solve the radical quintic functional equation
$$\begin{aligned} f\left( \root 5 \of {x^5+y^5}\right) = f(x)+f(y),\;\;\;x,y\in \mathbb {R}, \end{aligned}$$
for f a mapping from \(\mathbb {R}\) into a vector space. We also establish stability results in quasi-\(\beta \)-Banach spaces, and then the stability by using subadditive and subquadratic functions in (\(\beta , p\))-Banach spaces for this functional equation. In addition, we also present a counterexample that does not satisfy the stability based on Ulam’s question.

Keywords

Radical functional equations Subadditive and subquadratic functions Quasi-\(\beta \)-normed spaces Stability Counterexample 

Mathematics Subject Classification

65Q20 39B82 39B62 46H25 

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesIbn Tofail UniversityKenitraMorocco

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