• Title, Summary, Keyword: Functional equation

Search Result 714, Processing Time 0.036 seconds

ON THE SUPERSTABILITY OF SOME PEXIDER TYPE FUNCTIONAL EQUATION II

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

SUPERSTABILITY OF A GENERALIZED EXPONENTIAL FUNCTIONAL EQUATION OF PEXIDER TYPE

  • Lee, Young-Whan
    • Communications of the Korean Mathematical Society
    • /
    • v.23 no.3
    • /
    • pp.357-369
    • /
    • 2008
  • 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.

SOLUTION AND STABILITY OF AN EXPONENTIAL TYPE FUNCTIONAL EQUATION

  • Lee, Young-Whan;Kim, Gwang-Hui;Lee, Jae-Ha
    • The Pure and Applied Mathematics
    • /
    • v.15 no.2
    • /
    • pp.169-178
    • /
    • 2008
  • In this paper we generalize the superstability of the exponential functional equation proved by J. Baker et al. [2], that is, we solve an exponential type functional equation $$f(x+y)\;=\;a^{xy}f(x)f(y)$$ 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 $$|{\frac{f(x\;+\;y)}{{a^{xy}f(x)f(y)}}}\;-\;1|\;{\leq}\;{\delta}.$$

  • PDF

THE STABILITY OF A GENERALIZED CAUCHY FUNCTIONAL EQUATION

  • LEE, EUN HWI;CHOI, YOUNG HO;NA, YOUNG YOON
    • Honam Mathematical Journal
    • /
    • v.22 no.1
    • /
    • pp.37-46
    • /
    • 2000
  • We prove the stability of a generalized Cauchy functional equation of the form ; $$f(a_1x+a_2y)=b_1f(x)+b_2f(y)+w.$$ That is, we obtain a partial answer for the open problem which was posed by the Th.M Rassias and J. Tabor on the stability for a generalized functional equation.

  • PDF

APPROXIMATE PEXIDERIZED EXPONENTIAL TYPE FUNCTIONS

  • Lee, Young-Whan
    • The Pure and Applied Mathematics
    • /
    • v.19 no.2
    • /
    • pp.193-198
    • /
    • 2012
  • We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$. From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$.

APPROXIMATE ADDITIVE MAPPINGS IN 2-BANACH SPACES AND RELATED TOPICS: REVISITED

  • YUN, SUNGSIK
    • Korean Journal of Mathematics
    • /
    • v.23 no.3
    • /
    • pp.393-399
    • /
    • 2015
  • W. Park [J. Math. Anal. Appl. 376 (2011) 193-202] proved the Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. But there are serious problems in the control functions given in all theorems of the paper. In this paper, we correct the statements of these results and prove the corrected theorems. Moreover, we prove the superstability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces under the original given conditions.

STABILITY OF A JENSEN TYPE FUNCTIONAL EQUATION

  • Lee, Sang Han
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.14 no.1
    • /
    • pp.73-83
    • /
    • 2001
  • In this paper, we solve a Jensen type functional equation and prove the stability of the Jensen type functional equation.

  • PDF

HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION

  • Trif, Tiberiu
    • Bulletin of the Korean Mathematical Society
    • /
    • v.40 no.2
    • /
    • pp.253-267
    • /
    • 2003
  • In this paper we deal With the quadratic functional equation (equation omitted) deriving from an inequality of T. Popoviciu for convex functions. We solve this functional equation by proving that its solutions we the polynomials of degree at most two. Likewise, we investigate its stability in the spirit of Hyers, Ulam, and Rassias.