Generalized Hyers-Ulam Stability for a Mixed Quadratic - Quartic (QQ) Functional Equation in Quasi-Banach Spaces
K. Balamurugan
Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, Tamilnadu, India.
M. Arunkumar
Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, Tamilnadu, India.
P. Ravindiran *
Department of Mathematics, Arignar Anna Government Arts College, Villupuram - 605 602, Tamilnadu, India.
*Author to whom correspondence should be addressed.
Abstract
In this paper we establish the general solutions and investigate the Hyers - Ulam stability of the
following functional equation
f(3x + 2y + z) + f(3x + 2y - z) + f(3x - 2y + z) + f(3x - 2y - z)
= 72[f(x + y) + f(x - y)] + 18[f(x + z) + f(x - z)] + 8[f(y + z) + f(y - z)]
+ 24f(2x) + 4f(2y) - 240f(x) - 160f(y) - 48f(z)
in quasi-Banach spaces.
Keywords: Hyers-Ulam stability, quadratic mapping, quartic mapping, mixed type functional equation, quasi - Banach space, p - Banach space.