• Kyungpook Mathematical Journal
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• 제43권4호
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• pp.481-487
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• 2003

In this paper we study the Hyers-Ulam-Rassias stability of Popoviciu's functional equation in Banach modules over a Banach algebra.

• 호남수학학술지
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• 제27권1호
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• pp.51-68
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• 2005

In this paper we solve a generalized Popoviciu functional equation and investigate the stability of this equation.

• 대한수학회보
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• 제40권2호
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• pp.253-267
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• 2003

In this paper we deal With the quadratic functional equation (equation omitted) deriving from an inequality of T. Popoviciu for convex functions. We solve this functional equation by proving that its solutions we the polynomials of degree at most two. Likewise, we investigate its stability in the spirit of Hyers, Ulam, and Rassias.

• 대한수학회보
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• 제42권1호
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• pp.57-73
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• 2005

In this paper we solve a generalized quadratic Jensen type functional equation $m^2 f (\frac{x+y+z}{m}) + f(x) + f(y) + f(z) =n^2 [f(\frac{x+y}{n}) +f(\frac{y+z}{n}) +f(\frac{z+x}{n})]$ and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권2호
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• pp.161-172
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• 2011

In this paper we investigate the Hyers-Ulam stability of a Jensen type functional equation in multi-normed spaces and then extend the result to multi-normed left modules over a normed algebra A.