On the General Solution of a Quadratic Functional Equation and its Ulam Stability in Various Abstract Spaces

Shen, Yonghong¹ ; Lan, Yaoyao²

¹ School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, P. R. China
² Department of Mathematics and Finance, Chongqing University of Arts and Sciences, Yongchuan 402160, P. R. China

Journal of nonlinear sciences and its applications, Tome 7 (2014) no. 6, p. 368-378.

Résumé

In this paper, we establish the general solution of a new quadratic functional equation $f ( x -\frac{ y+z}{ 2} ) + f ( x + \frac{y-z}{ 2}) +f(x+z) = 3f(x)+ \frac{1}{ 2}f(y)+ \frac{3}{ 2}f(z)$. Next, the Ulam stability of this equation in a real normed space and a non-Archimedean space is studied, respectively.

Détail

DOI : 10.22436/jnsa.007.06.01

Classification : 39A30, 97I70
Keywords: General solution, Ulam stability, Quadratic functional equation, Normed space, Non-Archimedean space.

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