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

2019/06/07 by Sintunavarat, Wutiphol, Van Dung, Nguyen, Thanyacharoen, Anurak
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1906.03010

Abstract

In this paper, we study the generalized Hyers-Ulam stability of Euler-Lagrange type cubic functional equation of the form 2mf(x + my) + 2f(mx - y) = (m³ + m)[f(x+ y) + f(x - y)] + 2(m⁴ - 1)f(y) for all x,y ∈ X, where m is a fixed scalar such that m ≠ 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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