Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation

Abstract

Abstract. We prove uniqueness theorems concerning the functional inequalities in connection with an n -dimensional cubic-quadratic-additive equationby applying the direct method.Mathematics subject classification (2010): 39B82, 39B52.

On a functional equation that has the quadratic-multiplicative property

“…The problem of the stability of functional equations has been posed by Ulam [1]. Hyers [2] gave a positive answer for the stability of the Cauchy equation: From that time many other functional equations and inequalities have been studied (see [3][4][5][6][7][8][9]). Let E 1 and E 2 be real vector spaces.…”

Stability of an AQCQ functional equation in non-Archimedean (n, β)-normed spaces

“…The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem. A large list of references can be found in [4][5][6][7][8][9][10][11][12][13][14][15].…”

Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

“…Since that period, the corresponding area has become a very vibrant domain of research and stability problems for several functional equations have been extensively investigated by a number of authors (cf. [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]).…”