바로가기메뉴

본문 바로가기 주메뉴 바로가기

logo

  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

Article Contents

Prev Next
e-Submission

Vol.19 No.4

Citation Share

ON THE STABILITY OF A MIXED TYPE QUADRATIC AND CUBIC FUNCTIONAL EQUATION

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2012, v.19 no.4, pp.383-396
https://doi.org/10.7468/jksmeb.2012.19.4.383
Lee, Chang-Ju
Lee, Yang-Hi
Lee,, C. , & Lee,, Y. (2012). ON THE STABILITY OF A MIXED TYPE QUADRATIC AND CUBIC FUNCTIONAL EQUATION. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 19(4), 383-396, https://doi.org/10.7468/jksmeb.2012.19.4.383

Abstract

In this paper, we investigate a fuzzy version of stability for the functional equation <TEX>$$f(x+2y)-3f(x+y)+3f(x)-f(x-y)-3f(y)+3f(-y)=0$$</TEX> in the sense of M. Mirmostafaee and M. S. Moslehian.

keywords
fuzzy normed space, fuzzy almost cubic-quadratic mapping

Reference

1.

(1950). On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan, 2, 64-66. 10.2969/jmsj/00210064.

2.

(2003). Finite dimensional fuzzy normed linear spaces. J. fuzzy Math., 11(3), 687-705.

3.

(1994). Fuzzy linear operator and fuzzy normed linear spaces. Bull. Calcutta Math. Soc., 86, 429-436.

4.

(1994). A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl., 184, 431-436. 10.1006/jmaa.1994.1211.

5.

(1941). On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA, 27, 222-224. 10.1073/pnas.27.4.222.

6.

(1984). Fuzzy topological vector spaces II. Fuzzy Sets and Systems, 12, 143-154. 10.1016/0165-0114(84)90034-4.

7.

(1975). Fuzzy metric and statistical metric spaces. Kybernetica, 11, 326-334.

8.

(2008). On the stability of the monomial functional equation. Bull. Korean Math. Soc., 45, 397-403. 10.4134/BKMS.2008.45.2.397.

9.

(2000). On the Stability of Approximately Additive Mappings. Proc. Amer. Math. Soc., 128, 1361-1369. 10.1090/S0002-9939-99-05156-4.

10.

(2008). Fuzzy versions of Hyers-Ulam-Rassias theorem. Fuzzy Sets and Systems, 159, 720-729. 10.1016/j.fss.2007.09.016.

11.

(2009). On stability of a cubic functional equation in intu- itionistic fuzzy normed spaces. Chaos, Solitons & Fractals, 42, 2997-3005. 10.1016/j.chaos.2009.04.041.

12.

(1978). On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc., 72, 297-300. 10.1090/S0002-9939-1978-0507327-1.

13.

(2010). A mixed-type quadratic and cubic functional equation and its stability (61-71). Thai Journal of Mathematics Special Issue (Annual Meeting in Mathematics).

14.

A Collection of Mathematical Problems.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

e-Submission OA Policy