[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2022.35.2.149

A NOTE ON FUNCTIONAL INEQUALITY AND ADDITIVE MAPPING

Chang, Ick-Soon (Department of Mathematics, Chungnam National University)
Lee, Hyun-Wook (Department of Mathematics, Chungnam National University)
Kim, Hark-Mahn (Department of Mathematics, Chungnam National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.35, no.2, 2022 , pp. 149-159 More about this Journal

Abstract

In this note, we prove some theorems concerning the stability of functional inequality associated with additive mappings on quasi-𝛽-normed spaces.

Keywords

quasi- ${\beta}$ -normed space; stability; functional inequality;

Citations & Related Records

Reference

1	Y. Benyamini and J. Lindenstrauss, Geometric Nonlinear Functional Analysis, Vol. 1, Colloq. Publ. 48 Amer. Math. Soc., Providence, 2000.
2	P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436. DOI
3	D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci., U.S.A. 27 (1941), 222-224. DOI
4	J. Ratz, On inequalities associated with the Jordan-von Neumann functional equation, Aequationes Math., 66 (2003), 191-200. DOI
5	Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci., 14 (1991), 431-434. DOI
6	A. Gilanyi, Eine zur Parallelogrammgleichung aquivalente Ungleichung, Aequationes Math., 62 (2001), 303-309. DOI
7	A. Gilanyi, On a problem by K. Nikodem, Math. Inequal. Appl., 5 (2002), 707-710.
8	A. Najati and M. B. Moghimi, Stability of a functional equation deriving from quadratic and additive function in quasi-Banach spaces, J. Math. Anal. Appl., 337 (2008), 399-415. DOI
9	Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300. DOI
10	S. Rolewicz, Metric Linear Spaces, Reidel and Dordrecht, and PWN-Polish Sci., Publ. 1984.
11	S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960.
12	W. Fechner, Stability of a functional inequalities associated with the Jordan-von Neumann functional equation, Aequationes Math., 71 (2006), 149-161. DOI