• 제목/요약/키워드: cosine functional equation

검색결과 13건 처리시간 0.025초

COSINE FUNCTIONAL EQUATION IN SEVERAL VARIABLES

  • CHUNG, JAEYOUNG;KO, SEUNGJUN;SONG, SUNGHYUN
    • 호남수학학술지
    • /
    • 제27권1호
    • /
    • pp.43-49
    • /
    • 2005
  • Making use of a transparent way of convolution by tensor product of approximate identities we consider the cosine functional equation in several variables.

  • PDF

ON THE STABILITY OF THE COSINE TYPE FUNCTIONAL EQUATION

  • Kim, Gwang-Hui
    • 한국수학교육학회지시리즈B:순수및응용수학
    • /
    • 제14권1호
    • /
    • pp.7-14
    • /
    • 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).

  • PDF

THE STABILITY OF PEXIDERIZED COSINE FUNCTIONAL EQUATIONS

  • Kim, Gwang Hui
    • Korean Journal of Mathematics
    • /
    • 제16권1호
    • /
    • pp.103-114
    • /
    • 2008
  • In this paper, we investigate the superstability problem for the pexiderized cosine functional equations f(x+y) +f(x−y) = 2g(x)h(y), f(x + y) + g(x − y) = 2f(x)g(y), f(x + y) + g(x − y) = 2g(x)f(y). Consequently, we have generalized the results of stability for the cosine($d^{\prime}Alembert$) and the Wilson functional equations by J. Baker, $P.\;G{\check{a}}vruta$, R. Badora and R. Ger, and G.H. Kim.

  • PDF

ON THE SUPERSTABILITY OF SOME PEXIDER TYPE FUNCTIONAL EQUATION II

  • Kim, Gwang-Hui
    • 한국수학교육학회지시리즈B:순수및응용수학
    • /
    • 제17권4호
    • /
    • pp.397-411
    • /
    • 2010
  • In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

ON THE SUPERSTABILITY FOR THE p-POWER-RADICAL SINE FUNCTIONAL EQUATION

  • Gwang Hui Kim
    • Nonlinear Functional Analysis and Applications
    • /
    • 제28권3호
    • /
    • pp.801-812
    • /
    • 2023
  • In this paper, we investigate the superstability for the p-power-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)$$ from an approximation of the p-power-radical functional equation: $$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 and f, g, h are complex valued functions. Furthermore, the obtained results are extended to Banach algebras.

SUPERSTABILITY OF THE p-RADICAL TRIGONOMETRIC FUNCTIONAL EQUATION

  • Kim, Gwang Hui
    • Korean Journal of Mathematics
    • /
    • 제29권4호
    • /
    • pp.765-774
    • /
    • 2021
  • In this paper, we solve and investigate the superstability of the p-radical functional equations $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}f(x)g(y),\\f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)f(y),$$ which is related to the trigonometric(Kim's type) functional equations, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebras.

THE STABILITY OF THE GENERALIZED SINE FUNCTIONAL EQUATIONS III

  • Kim, Gwang Hui
    • 충청수학회지
    • /
    • 제20권4호
    • /
    • pp.465-476
    • /
    • 2007
  • The aim of this paper is to investigate the stability problem bounded by function for the generalized sine functional equations as follow: $f(x)g(y)=f(\frac{x+y}{2})^2-f(\frac{x+{\sigma}y}{2})^2\\g(x)g(y)=f(\frac{x+y}{2})^2-f(\frac{x+{\sigma}y}{2})^2$. As a consequence, we have generalized the superstability of the sine type functional equations.

  • PDF

ON THE SUPERSTABILITY OF THE p-RADICAL SINE TYPE FUNCTIONAL EQUATIONS

  • Kim, Gwang Hui
    • 한국수학교육학회지시리즈B:순수및응용수학
    • /
    • 제28권4호
    • /
    • pp.387-398
    • /
    • 2021
  • In this paper, we will find solutions and investigate the superstability bounded by constant for the p-radical functional equations as follows: $f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=\;\{(i)\;f(x)f(y),\\(ii)\;g(x)f(y),\\(iii)\;f(x)g(y),\\(iv)\;g(x)g(y).$ with respect to the sine functional equation, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebra.