[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b190017

STABILITY OF PARTIALLY PEXIDERIZED EXPONENTIAL-RADICAL FUNCTIONAL EQUATION

Choi, Chang-Kwon (Department of Mathematics and Hwangryong Talent Education Institute Kunsan National University)

Publication Information

Bulletin of the Korean Mathematical Society / v.58, no.2, 2021 , pp. 269-275 More about this Journal

Abstract

Let ℝ be the set of real numbers, f, g : ℝ → ℝ and �� ≥ 0. In this paper, we consider the stability of partially pexiderized exponential-radical functional equation $$$f({\sqrt[n$ $]$ ${x^N+y^N}})=f(x)g(y)$$$ for all x, y ∈ ℝ, i.e., we investigate the functional inequality $$$\|f({\sqrt[n$ $]$ ${x^N+y^N}})-f(x)g(y)\|{\leq}{\epsilon}$$$ for all x, y ∈ ℝ.

Keywords

Exponential functional equation; monomial functional equation; pexiderized functional equation; radical functional equation; stability;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

1	J. Chung, C.-K. Choi, and B. Lee, On bounded solutions of Pexider-exponential functional inequality, Honam Math. J. 35 (2013), no. 2, 129-136. https://doi.org/10.5831/HMJ.2013.35.2.129 DOI
2	D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222 DOI
3	D. H. Hyers, G. Isac, and T. M. Rassias, Stability of functional equations in several variables, Progress in Nonlinear Differential Equations and their Applications, 34, Birkhauser Boston, Inc., Boston, MA, 1998. https://doi.org/10.1007/978-1-4612-1790-9 DOI
4	L. Szekelyhidi, On a theorem of Baker, Lawrence and Zorzitto, Proc. Amer. Math. Soc. 84 (1982), no. 1, 95-96. https://doi.org/10.2307/2043816 DOI
5	S. M. Ulam, A collection of mathematical problems, Interscience Tracts in Pure and Applied Mathematics, no. 8, Interscience Publishers, New York, 1960.
6	J. Brzdek, Remarks on solutions to the functional equations of the radical type, Adv. Theory Nonlinear Anal. Appl. 1 (2017), 125-135.
7	C.-K. Choi, Stability of an exponential-monomial functional equation, Bull. Aust. Math. Soc. 97 (2018), no. 3, 471-479. https://doi.org/10.1017/S0004972718000011 DOI
8	J. A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), no. 3, 411-416. https://doi.org/10.2307/2043730 DOI
9	J. Baker, J. Lawrence, and F. Zorzitto, The stability of the equation f(x + y) = f(x)f(y), Proc. Amer. Math. Soc. 74 (1979), no. 2, 242-246. https://doi.org/10.2307/2043141 DOI