• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.429-445
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• 2004

In this paper we investigate the generalized Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(x,y)){\;}={\;}\phi(x,y)f(x,y)$, where x, y lie in the set S. As a consequence we obtain stability in the sense of Hyers, Ulam, Rassias, Gavruta, for some well-known equations such as the gamma, beta and G-function type equations.

• Korean Journal of Mathematics
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• 제24권2호
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• pp.297-305
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• 2016

In this paper, by using fixed point theorem, we obtain the stability of the following functional equations $$f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)f(p,q)h(r,s)\\f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)g(p,q)h(r,s)$$, where G is a commutative semigroup, ${\theta}:G^4{\rightarrow}{\mathbb{R}}_k$ a function and f, g, h are functionals on $G^2$.

• 대한수학회논문집
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• 제20권2호
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• pp.321-338
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• 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.

• 충청수학회지
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• 제32권1호
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• pp.29-46
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• 2019

We introduce a generalized cubic functional equation and investigate the Hyers-Ulam stability of the cubic functions as solutions to the generalized cubic functional equation on a quasi-fuzzy anti-${\beta}$-Banach space by both the direct method and the fixed point method.

• 대한수학회보
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• 제43권3호
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• pp.531-541
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• 2006

[ $C\u{a}dariu$ ] and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we adopt the idea of $C\u{a}dariu$ and Radu to prove the Hyers-Ulam-Rassias stability of the quadratic functional equation for a large class of functions from a vector space into a complete ${\gamma}-normed$ space.

• Journal of Animal Science and Technology
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• 제64권1호
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• pp.155-165
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• 2022

As pork consumption increases, rapid and accurate determination of porcine carcass grades at abattoirs has become important. Non-destructive, automated inspection methods have improved slaughter efficiency in abattoirs. Furthermore, the development of a calibration equation suitable for non-destructive inspection of domestic pig breeds may lead to rapid determination of pig carcass and more objective pork grading judgement. In order to increase the efficiency of pig slaughter, the correct estimation of the automated-method that can accommodate the existing pig carcass judgement should be made. In this study, the previously developed calibration equation was verified to confirm whether the estimated traits accord with the actual measured traits of pig carcass. A total of 1,069,019 pigs, to which the developed calibration equation, was applied were used in the study and the optimal estimated regression equation for actual measured two traits (backfat thickness and hot carcass weight) was proposed using the estimated traits. The accuracy of backfat thickness and hot carcass weight traits in the estimated regression models through stepwise regression analysis was 0.840 (R²) and 0.980 (R²), respectively. By comparing the actually measured traits with the estimated traits, we proposed optimal estimated regression equation for the two measured traits, which we expect will be a cornerstone for the Korean porcine carcass grading system.

• Korean Journal of Mathematics
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• 제20권1호
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• pp.33-46
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• 2012

Using the direct method, we prove the Hyers-Ulam stability of the orthogonally additive-quartic functional equation (0.1) $f(2x+y)+f(2x-y)=4f(x+y)+4f(x-y)+10f(x)+14f(-x)-3f(y)-3f(-y)$ for all $x$, $y$ with $x{\perp}y$, in non-Archimedean Banach spaces. Here ${\perp}$ is the orthogonality in the sense of R$\ddot{a}$tz.

• 충청수학회지
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• 제22권1호
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• pp.31-37
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• 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.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 춘계 학술발표회 논문집
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• pp.31-36
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• 2003

Using a short time expansion of the fundamental solution of heat equation by analysis of Wiener functional with the help of Malliavin calculus, we obtain the asymptotic expansion of the mean distance of Brownian motion on Riemannian manifolds.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.445-453
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• 2007

This paper deals with the approximate controllability for the nonlinear functional differential equations with time delay and studies a variation of constant formula for solutions of the given equations.