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Zbl 1130.39025
Lee, Young-Su; Chung, Soon-Yeong
Stability of a Jensen type functional equation.
(English)
[J] Banach J. Math. Anal. 1, No. 1, 91-100, electronic only (2007). ISSN 1735-8787/e

The authors solve the following Jensen type functional equation $$mf\left(\frac{x+y+z}{m}\right)+f(x)+f(y)+f(z)= n \left[ f\left(\frac{x+y}{n}\right) + f\left(\frac{y+z}{n}\right) + f\left(\frac{z+x}{n}\right)\right],$$ where $m$ and $n$ are nonnegative integers with $(m,n)\neq (1,1)$. Moreover, they prove the stability of the above functional equation in the spirit of {\it D.H. Hyers, G. Isac} and {\it Th.M. Rassias} [Stability of functional equations in several variables. Progress in Nonlinear Differential Equations and their Applications. 34. Boston, MA: Birkhäuser (1998; Zbl 0907.39025)].
MSC 2000:
*39B82 Stability, separation, extension, and related topics
39B22 Functional equations for real functions
39B52 Functional equations for functions with more general domains

Keywords: Hyers-Ulam-Rassias stability; Jensen functional equation

Citations: Zbl 0907.39025

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