[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7468/jksmeb.2019.26.4.267

A FIXED POINT APPROACH TO THE STABILITY OF AN ADDITIVE-CUBIC-QUARTIC FUNCTIONAL EQUATION

Lee, Yang-Hi (Department of Mathematics Education, Gongju National University of Education)

Publication Information

The Pure and Applied Mathematics / v.26, no.4, 2019 , pp. 267-276 More about this Journal

Abstract

In this paper, we investigate the stability of an additive-cubic-quartic functional equation f(x + 2y) - 4f(x + y) + 6f(x) - 4f(x - y) + f(x - 2y) - 12f(y) - 12f(-y) = 0 by applying the fixed point theory in the sense of L. Cădariu and V. Radu.

Keywords

stability; additive-cubic-quartic functional equation; fixed point theory;

Citations & Related Records

Reference

1	Th.M. Rassias: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72 (1978), 297-300. DOI
2	I.A. Rus: Principles and Applications of Fixed Point Theory. Ed. Dacia, Cluj-Napoca 1979(in Romanian).
3	R. Saadati, M.M. Zohdi & S.M. Vaezpour: Nonlinear L-random stability of an ACQ functional equation. J. Inequal. Appl. 2011 Article ID 194394.
4	S.M. Ulam: A Collection of Mathematical Problems. Interscience, New York, 1960.
5	Z. Wang, X. Li & Th.M. Rassias: Stability of an additive-cubic-quartic functional equation in multi-Banach spaces. Abstr. Appl. Anal. 2011 Article ID 536520.
6	T. Aoki: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan 2 (1950), 64-66. DOI
7	J. Baker: A general functional equation and its stability. Proc. Natl. Acad. Sci. 133 (2005), no. 6, 1657-1664.
8	L. Cadariu & V. Radu: Fixed points and the stability of Jensen's functional equation. J. Inequal. Pure Appl. Math. 4 (2003), no. 1, Art. 4.
9	L. Cadariu & V. Radu: On the stability of the Cauchy functional equation: a fixed point approach in Iteration Theory. Grazer Mathematische Berichte, Karl-Franzens-Universitaet, Graz, Graz, Austria 346 (2004), 43-52.
10	L. Cadariu & V. Radu: Fixed points and the stability of quadratic functional equations. An. Univ. Timisoara Ser. Mat.-Inform. 41 (2003), 25-48.
11	Y.J. Cho & R. Saadati: Lattictic non-archimedean random stability of ACQ functional equation. Adv. Differ. Equ. 2011, no. 1, 31. DOI
12	J.B. Diaz & B. Margolis: A fixed point theorem of the alternative for contractions on a generalized complete metric space. Bull. Amer. Math. Soc. 74 (1968), 305-309. DOI
13	P. Gavruta: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184 (1994), 431-436. DOI
14	M.E. Gordji, Y.J. Cho, H. Khodaei & M. Ghanifard: Solutions and stability of generalized mixedtType QCA-functional equations in random normed spaces. Annals of the Alexandru Ioan Cuza University-Mathematics 59 (2013), no. 2, 299-320. DOI
15	M.E. Gordji, S.K. Gharetapeh, C. Park & S. Zolfaghri: Stability of an additive-cubic-quartic functional equation. Adv. Differ. Equ. 2009 Article ID 395693.
16	D.H. Hyers: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224. DOI
17	Y.-H. Lee & S.-M. Jung: Generalized Hyers-Ulam stability of some cubic-quadratic-additive type functional equations. (2000), submitted.
18	J M. Rassias, M. Arunkumar, E. Sathya & N. Mahesh Kumar: Solution and Stability of an ACQ Functional Equation in Generalized 2-Normed Spaces. Intern. J. Fuzzy Mathematical Archive 7 (2015), 213-224.