• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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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.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.393-399
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• 2015

W. Park [J. Math. Anal. Appl. 376 (2011) 193-202] proved the Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. But there are serious problems in the control functions given in all theorems of the paper. In this paper, we correct the statements of these results and prove the corrected theorems. Moreover, we prove the superstability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces under the original given conditions.

• The Pure and Applied Mathematics
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• v.14 no.1 s.35
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• pp.7-14
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• 2007

The aim of this paper is to study the superstability problem of the cosine type functional equation f(x+y)+f(x+${\sigma}y$)=2g(x)g(y).

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.477-486
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• 2000

In this paper, we investigate the Hyers-Ulam-Rassias stability of a quadratic functional equation f(x+y+z)+f(x+y)+f(y-z)+f(z-x)=3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam stability of the equation on restricted (unbounded) domains.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.653-658
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• 1998

In this paper, we investigate the Hyers-Ulam stability of the (p,k)-MP functional equation.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.91-102
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• 2009

Using the fixed point method, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the 3-variable Cauchy functional equation.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.91-106
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• 2012

In this paper, we prove the Hyers-Ulam stability of the Jensen functional equation in fuzzy Banach algebras by using fixed point method and by using direct method.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.163-172
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• 2007

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

• Kyungpook Mathematical Journal
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• v.43 no.4
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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.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.837-844
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• 2002

In this paper, we obtain the Hyers-Ulam Stability for the difference equations of the form f(x + 1) = $\Gamma$(x)f(x), which is the reciprocal functional equation of the double gamma function.