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SUPERSTABILITY OF A GENERALIZED EXPONENTIAL FUNCTIONAL EQUATION OF PEXIDER TYPE
Lee, Young-Whan Korean Mathematical Society 2008 대한수학회논문집 Vol.23 No.3
We obtain the superstability of a generalized exponential functional equation f(x+y)=E(x,y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: $$|\frac{f(x+y)}{(E(x,y)g(x)f(y)}-1|{\leq}{\varphi}(x,y)$$ where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy's gamma-beta functional equation.
ON THE STABILITY OF THE GENERAL SEXTIC FUNCTIONAL EQUATION
Ick-Soon Chang,Yang-Hi Lee,Jaiok Roh 충청수학회 2021 충청수학회지 Vol.34 No.3
The general sextic functional equation is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation and the quintic functional equation. In this paper, motivating the method of Găvruta [J. Math. Anal. Appl., 184 (1994), 431--436], we will investigate the stability of the general sextic functional equation.
SUPERSTABILITY OF A GENERALIZED TRIGONOMETRIC FUNCTIONAL EQUATION
Kim Gwang Hui 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.2
We will investigate the superstability of the trigonometric functional equation from the following Pexider type functional equation: f(x+y)−f(x−y) = λ·g(x)h(y), λ is constant, which is a trigonometric functional equation mixed by the sine and cosine function. More- over, the equation can be considered by the mixed functional equation of the hyperbolic trigonometric functions, several exponential type functions, and Jensen type equation.
ON THE SUPERSTABILITY OF SOME PEXIDER TYPE FUNCTIONAL EQUATION II
김광휘 한국수학교육학회 2010 純粹 및 應用數學 Vol.17 No.4
In this paper, we will investigate the superstability for the sine func-tional equation from the following Pexider type functional equation :f(x + y) ¡ g(x ¡ y) = λ·h(x)k(y) λ : constant;which can be considered an exponential type functional equation, the mixed func-tional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.
Jin, Sun-Sook,Lee, Yang-Hi The Youngnam Mathematical Society 2020 East Asian mathematical journal Vol.36 No.1
In this paper, we investigate Hyers-Ulam-Rassias stability of an additive-quartic functional equation, of a quadratic-quartic functional equation, and of a cubic-quartic functional equation.
진선숙,이양희 영남수학회 2020 East Asian mathematical journal Vol.36 No.1
In this paper, we investigate Hyers-Ulam-Rassias stability of an additive-quartic functional equation, of a quadratic-quartic functional equation, and of a cubic-quartic functional equation.
Fahandari Heidar Kermanizadeh,Majani Hamid,Jang Sun Young,Park Choonkil 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.3
In this paper, we introduce the following functional equation \begin{equation*}\label{000} \sum_{i=0}^{k}(-1)^i\left(% \begin{array}{c} k \\ i \\ \end{array}% \right)f(x+(j-i)y)=k!f(y) . \end{equation*} where $k\in\mathbb{N}$ and $j=[\frac{k+1}{2}]$. We achieve the general solution of the above functional equation.
정재영(Jaeyoung Chung),강한성(Hansung Kang),고수빈(Subin Ko),김재욱(Jaewook Kim),여태민(Taemin Yeo),이건희(Gunhee Lee) 한국과학영재교육학회 2011 과학영재교육 Vol.3 No.3
본 연구에서는 고등학교 수준에서 다루어질 수 있는 주제로서 문제 해결력을 위한 좋은 과제인 함수방정식을 다루고 있다. 이 분야에서 특히 중요한 위치를 차지하고 있는 방정식인 코시함수방 정식과 그리고 이와 연관된 젠센함수방정식, 펙시드함수방정식, 로그함수방정식 등이 제한된 영역 에서 만족할 때 이 방정식들의 일반해와 정칙해를 구한다. In this paper the authors deal with functional equations which is a good research topic for high school students. In particular, they consider the Cauchy equation, Pexider equation, Jensen equation and logarithmic functional equation satisfied in the complements of rhombi or in the half planes, and find the general solutions and the regular solutions of the equations.
STABILITY OF FUNCTIONAL EQUATIONS RELATED TO THE EXPONENTIAL AND BETA FUNCTIONS
이영환 한국수학교육학회 2010 純粹 및 應用數學 Vol.17 No.4
In this paper we obtain the Hyers-Ulam stability of functional equations f(x + y) = f(x) + f(y) + ln a2xy-¹and f(x + y) = f(x) + f(y) + ln ¯(x; y)-¹which is related to the exponential and beta functions.
SOLUTION AND STABILITY OF AN EXPONENTIAL TYPE FUNCTIONAL EQUATION
이영환,김광휘,이재하 한국수학교육학회 2008 純粹 및 應用數學 Vol.15 No.2
In this paper we generalize the superstability of the exponential func- tional equation proved by J. Baker et al. [2], that is, we solve an exponential type functional equation f(x + y) = axyf(x)f(y) and obtain the superstability of this equation. Also we generalize the stability of the exponential type equation in the spirt of R. Ger[4] of the following setting : f(x + y) axyf(x)f(y) ¡ 1· ±: