Browse > Article
http://dx.doi.org/10.14403/jcms.2016.29.1.103

STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY IN BANACH SPACES  

Chung, Sang-Cho (Department of Mathematics Education, Mokwon University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.29, no.1, 2016 , pp. 103-108 More about this Journal
Abstract
In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(x_1+x_2)+f(x_2+x_3)+{\cdots}+f(x_n+x_1){\parallel}{\leq}{\parallel}tf(x_1+x_2+{\cdots}+x_n){\parallel}$$ in Banach spaces where a positive integer $n{\geq}3$ and a real number t such that $2{\leq}t$ < n.
Keywords
additive functional inequality; Banach space;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 S.-C. Chung, On the stability of a genaral additive functional inequality in Banach spaces, J. Chungcheong Math. Soc. 26 (2013), no. 4, 907-913.   DOI
2 D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. 27 (1941), 222-224.   DOI
3 J. R. Lee, C. Park, and D. Y. Shin, Stability of an additive functional inequality in proper CQ*-algebras, Bull. Korean Math. Soc. 48 (2011), 853-871.   DOI
4 C. Park, Y. S. Cho, and M.-H. Han, Functional inequalities associated with Jordan-von Neumann-type additive functional equations, J. Inequal. Appl. 2007 (2007) Article ID 41820, 13 pages.
5 S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ., New York, 1960.