On alienation of two functional equations of quadratic type

Abstract

We deal with an alienation problem for an Euler-Lagrange type functional equation f(alpha x + beta y) + f(alpha x - beta y) = 2 alpha(2)f(x) + 2 beta(2)f(y) assumed for fixed nonzero real numbers alpha, alpha, 1 not equal alpha(2) not equal beta(2), and the classic quadratic functional equation g(x + y) + g(x - y) = 2g(x) + 2g(y). We were inspired by papers of Kim et al. (Abstract and applied analysis, vol. 2013, Hindawi Publishing Corporation, 2013) and Gordji and Khodaei (Abstract and applied analysis, vol. 2009, Hindawi Publishing Corporation, 2009), where the special case g = gamma f was examined.