• Title/Summary/Keyword: Pexider equation

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ORTHOGONAL PEXIDER HOM-DERIVATIONS IN BANACH ALGEBRAS

  • Vahid Keshavarz;Jung Rye Lee;Choonkil Park
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.1
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    • pp.95-105
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    • 2023
  • In the present paper, we introduce a new system of functional equations, known as orthogonal Pexider hom-derivation and Pexider hom-Pexider derivation (briefly, (Pexider) hom-derivation). Using the fixed point method, we investigate the stability of Pexider hom-derivations and (Pexider) hom-derivations on Banach algebras.

ON THE STABILITY OF PEXIDER TYPE TRIGONOMETRIC FUNCTIONAL EQUATIONS

  • Kim, Gwang Hui
    • Korean Journal of Mathematics
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    • v.16 no.3
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    • pp.369-378
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    • 2008
  • The aim of this paper is to study the stability problem for the pexider type trigonometric functional equation f(x + y) − f(x−y) = 2g(x)h(y), which is related to the d'Alembert, the Wilson, the sine, and the mixed trigonometric functional equations.

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ON THE SUPERSTABILITY OF SOME PEXIDER TYPE FUNCTIONAL EQUATION II

  • Kim, Gwang-Hui
    • The Pure and Applied Mathematics
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    • v.17 no.4
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    • pp.397-411
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    • 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.

A GENERALIZATION OF THE HYERS-ULAM-RASSIAS STABILITY OF A FUNCTIONAL EQUATION OF DAVISON

  • Jun, Kil-Woung;Jung, Soon-Mo;Lee, Yang-Hi
    • Journal of the Korean Mathematical Society
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    • v.41 no.3
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    • pp.501-511
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    • 2004
  • We prove the Hyers-Ulam-Rassias stability of the Davison functional equation f($\chi$y) + f($\chi$ + y) = f($\chi$y + $\chi$) + f(y) for a class of functions from a ring into a Banach space and we also investigate the Davison equation of Pexider type.

ON THE SUPERSTABILITY OF THE PEXIDER TYPE SINE FUNCTIONAL EQUATION

  • Kim, Gwang Hui
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.1
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    • pp.1-18
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    • 2012
  • The aim of this paper is to investigate the superstability of the pexider type sine(hyperbolic sine) functional equation $f(\frac{x+y}{2})^{2}-f(\frac{x+{\sigma}y}{2})^{2}={\lambda}g(x)h(y),\;{\lambda}:\;constant$ which is bounded by the unknown functions ${\varphi}(x)$ or ${\varphi}(y)$. As a consequence, we have generalized the stability results for the sine functional equation by P. M. Cholewa, R. Badora, R. Ger, and G. H. Kim.

SUPERSTABILITY OF THE GENERALIZED PEXIDER TYPE EXPONENTIAL EQUATION IN ABELIAN GROUP

  • Kim, Gwang Hui
    • Korean Journal of Mathematics
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    • v.20 no.2
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    • pp.213-223
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    • 2012
  • In this paper, we will prove the superstability of the following generalized Pexider type exponential equation $${f(x+y)}^m=g(x)h(y)$$, where $f,g,h\;:\;G{\rightarrow}\mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here G is an Abelian group (G, +), and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G$\check{a}$vruta's result in 1994 and G. H. Kim's results in 2011.