• Communications of the Korean Mathematical Society
• /
• v.20 no.2
• /
• pp.321-338
• /
• 2005

In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(X))\;=\;\phi(X)f(X)$, where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers, Ulam, Rassias, and Gavruta for many other equations such as the gamma, beta, Schroder, iterative, and G-function type's equations.

• Journal of applied mathematics & informatics
• /
• v.37 no.1_2
• /
• pp.53-63
• /
• 2019

In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.

• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.4
• /
• pp.315-327
• /
• 2022

In this paper, we investigate the transferred superstability for the p-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from the p-radical functional equations: $$f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)g(y),\;\\f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)h(y),$$ where p is an odd positive integer, λ is a positive real number, and f is a complex valued function. Furthermore, the results are extended to Banach algebras. Therefore, the obtained result will be forced to the pre-results(p=1) for this type's equations, and will serve as a sample to apply it to the extension of the other known equations.

• Journal of the Chungcheong Mathematical Society
• /
• v.17 no.1
• /
• pp.29-45
• /
• 2004

We prove the Cauchy-Rassias stability of cyclic functional equations in Banach modules over a unital $C^*$-algebra.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.4
• /
• pp.515-523
• /
• 2007

In this paper, we investigate the Hyers-Ulam-Rassias stability of generalized Jensen type quadratic functional equations in Banach spaces.

• Communications of the Korean Mathematical Society
• /
• v.23 no.4
• /
• pp.567-575
• /
• 2008

In this article we prove the Hyers.Ulam stability of trigonometric functional equations.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.315-330
• /
• 2007

In this paper, some hybrid fixed point theorems are proved which are further applied to first and second order neutral functional differential equations for proving the existence results for the extremal solutions under the mixed Lipschitz, compactness and monotonic conditions.

• Journal of applied mathematics & informatics
• /
• v.6 no.3
• /
• pp.929-935
• /
• 1999

By applications of the stability for a class of functional equa-tions we obtain the hyers-Ulam stability for the equations of the form g($\chi$+y)=kg($\chi$)g(y) in the following setting; ｜g($\chi$+y)-kg($\chi$)g(y)｜$\leq$$\Delta$($\chi$,y).

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.1
• /
• pp.31-37
• /
• 2009

In this paper, we obtain the generalized Hyers-Ulam stability of a functional equation and a system of functional equations on Jensen-quadratic mappings.

• The Pure and Applied Mathematics
• /
• v.22 no.4
• /
• pp.365-374
• /
• 2015

In this paper, we solve the additive ρ-functional equations