• 대한수학회지
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• 제41권3호
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• pp.501-511
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• 2004

We prove the Hyers-Ulam-Rassias stability of the Davison functional equation f($\chi$y) + f($\chi$ + y) = f($\chi$y + $\chi$) + f(y) for a class of functions from a ring into a Banach space and we also investigate the Davison equation of Pexider type.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.377-392
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• 2004

In the present paper, we obtain the Hyers-Ulam-Rassias stability in the sense of Gavruta for the general quadratic functional equation f(χ + y + z) + f(χ - y) + f(χ - z) = f(χ - y - z) + f(χ + y) + f(χ + z).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권4호
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• pp.323-335
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• 2004

In this paper, we solve the general solution of a modified additive and quadratic functional equation f(χ + 3y) + 3f(χ-y) = f(χ-3y) + 3f(χ+y) in the class of functions between real vector spaces and obtain the Hyers-Ulam-Rassias stability problem for the equation in the sense of Gavruta.

• Kyungpook Mathematical Journal
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• 제48권4호
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• pp.705-720
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• 2008

In this paper, we obtain the Hyers-Ulam-Rassias stability of a bi-Jensen functional equation $4f(\frac {x+y}{2},\;\frac {z+w}{2})=f(x,z)+f(x,w)+f(y,z)+f(y,w)$.

• 충청수학회지
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• 제21권2호
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• pp.197-208
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• 2008

In this paper, we obtain the Hyers-Ulam-Rassias stability of a Cauchy-Jensen functional equation $$f(x+y,z)-f(x,z)-f(y,z)=0,\\2f(x,\frac{y+z}2)-f(x,y)-f(x,z)=0$$ in the spirit of Th. M. Rassias.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.371-380
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• 2002

In this paper we obtain the general solution of a quadratic Jensen type functional equation : (equation omitted) and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.

• East Asian mathematical journal
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• 제30권3호
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• pp.271-281
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• 2014

In this paper, we consider the following cubic functional equation f(3x + y) + f(3x - y) = f(x + 2y) + 2f(x - y) + 2f(3x) - 3f(x) - 6f(y) and prove the generalized Hyers-Ulam stability for it in fuzzy normed spaces.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.133-144
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• 2020

We will prove the generalized Hyers-Ulam stability of cubic-quadratic-additive type functional equations and general cubic functional equations whose solutions are cubic-quadratic-additive mappings and general cubic mappings, respectively.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권2호
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• pp.167-178
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• 2009

In this paper, we obtain the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation f(x+y, z)-f(x, z)-f(y, z)=0, $$2f\;x,\;{\frac{y+z}{2}}-f(x,\;y)-f(x,\;z)=0$$ in the spirit of P. $G{\breve{a}}vruta$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권3호
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• pp.297-306
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• 2009

In this paper, we obtain the general solution and the generalized HyersUlam stability theorem for an additive functional equation $af(x+y)+2f({\frac{x}{2}}+y)+2f(x+{\frac{y}{2})=(a+3)[f(x)+f(y)]$for any fixed integer a.