Stability of a generalized quadratic functional equation with Jensen type
Bull. Korean Math. Soc. 2005 Vol. 42, No. 1, 57-73
Published online March 1, 2005
Young Whan Lee
Daejeon University
Abstract : In this paper we solve a generalized quadratic Jensen type functional equation $$ \align &m^2f\left(\frac{x + y + z}{m}\right) + f(x)+f(y)+f(z)\\ &= n^2 \left[f\left(\frac{x + y}{n}\right) + f\left(\frac{y + z}{n}\right) + f\left(\frac{z + x}{n}\right)\right] \endalign $$ and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and G\u{a}vruta.
Keywords : hyers-ulam-rassias stability, quadratic functional equation, Popoviciu functional equation
MSC numbers : 39B22, 39B72
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