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Stability of a Jensen type functional equation. (English) Zbl 1130.39025

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 D.H. Hyers, G. Isac and 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:

39B82 Stability, separation, extension, and related topics for functional equations
39B22 Functional equations for real functions
39B52 Functional equations for functions with more general domains and/or ranges

Citations:

Zbl 0907.39025
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