Stability of an ACQ-functional equation in various matrix normed spaces

Abstract

Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of the following additive-cubic-quartic (ACQ ) functional equationin matrix Banach spaces. Furthermore, using the fixed point method, we also prove the Hyers-Ulam stability of the above functional equation in matrix fuzzy normed spaces.

Stability on Quinquevigintic Functional Equation in Different Spaces

“…During the last eight decades, the stability problems of various functional equations such as additive [14], [18], [26], quadratic [22], [31], cubic [10], [28], [33], quartic [11], [15], [27] and mixed types [12], [37] have been investigated by many mathematicians.…”

Trevigintic and quattuorvigintic functional equations in matrix normed spaces

“…This terminology may also be applied to the cases of other functional equations [2,3,10,13,16,19,20,23]. Also, the generalized Hyers-Ulam stability of functional equations and inequalities in matrix normed space has been studied by number of authors [7,8,15,18,22].…”

Stability of Generalized Cubic Functional Equation in Matrix Normed Spaces

“…Rassias [6] were the first to provide applications of stability theory of functional equations for the proof of new fixed point theorems with applications. By using the fixed point method, the stability of several functional equations and inequalities in matrix normed spaces have been extensively investigated by number of authors [20,19,8,16,10,13].…”