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On a Jensen-cubic functional equation and its Hyers–Ulam stability

Research paper by Pei Sheng Ji, Shu Juan Zhou, Hai Yan Xue

Indexed on: 05 Dec '15Published on: 05 Dec '15Published in: Acta Mathematica Sinica, English Series



Abstract

In this paper, we obtain the general solution and stability of the Jensen-cubic functional equation \(f\left( {\frac{{{x_1} + {x_2}}}{2},{\kern 1pt} 2{y_1} + {y_2}} \right) + f\left( {\frac{{{x_1} + {x_2}}}{2},{\kern 1pt} 2{y_1} - {y_2}} \right)\) = f(x1, y1+y2)+f(x1, y1−y2)+6f(x1, y1)+f(x2, y1+y2) + f(x2, y1−y2) + 6f(x2, y1).