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arXiv · 1906.03010

Stability of Euler-Lagrange type cubic functional equations in quasi-Banach spaces

Wutiphol Sintunavarat·Nguyen Van Dung·Anurak Thanyacharoen
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Abstract

In this paper, we study the generalized Hyers-Ulam stability of Euler-Lagrange type cubic functional equation of the form \begin{align*} 2mf(x + my) + 2f(mx - y) = (m^3 + m)[f(x+ y) + f(x - y)] + 2(m^4 - 1)f(y) \end{align*} for all $x,y \in X$, where $m$ is a fixed scalar such that $m \neq 0,1$, and $f$ is a map from a quasi-normed space $X$ to a quasi-Banach space $Y$ over the same field with $X$ by applying the alternative fixed point theorem.

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Wutiphol Sintunavarat, Nguyen Van Dung, Anurak Thanyacharoen. 2019-06-07. Stability of Euler-Lagrange type cubic functional equations in quasi-Banach spaces. https://arxiv.org/abs/1906.03010

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