A Functional Equation Having Monomials and Its Stability

M. E. Gordji (), H. Khodaei () and Themistocles M. Rassias ()
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M. E. Gordji: Semnan University
H. Khodaei: Malayer University
Themistocles M. Rassias: National Technical University of Athens

A chapter in Handbook of Functional Equations, 2014, pp 181-197 from Springer

Abstract: Abstract We use some results about the Fréchet functional equation to consider the following functional equation: $$\begin{aligned} f\left(\left(\sum_{i=1}^{m}a_ix_i^p\right)^\frac{1}{p}\right)=\sum_{i=1}^{m}a_if(x_i).\end{aligned}$$ We also apply a fixed point method and homogeneous functions of degree α to investigate some stability results for this functional equation in β-Banach spaces.

Keywords: Frechet functional equation; Homogeneous functions; Dynamical systems; Hyers–Ulam–Rassias stability; Fixed point theorem (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4939-1286-5_9

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