Browse > Article
http://dx.doi.org/10.5666/KMJ.2014.54.3.401

Hyers-Ulam Stability of Jensen Functional Equation in p-Banach Spaces  

Kim, Hark-Mahn (Department of Mathematics, Chungnam National University)
Jun, Kil-Woung (Department of Mathematics, Chungnam National University)
Son, Eunyoung (Department of Mathematics, Chungnam National University)
Publication Information
Kyungpook Mathematical Journal / v.54, no.3, 2014 , pp. 401-411 More about this Journal
Abstract
In this paper, we prove the generalized Hyers-Ulam stability of the following Jensen type functional equation $$f(\frac{x-y}{n}+z)+f(\frac{y-z}{n}+x)+f(\frac{z-x}{n}+y)=f(x)+f(y)+f(z)$$ in p-Banach spaces for any fixed nonzero integer n.
Keywords
Stability; Jensen functional equation; Quasi-normed spaces; p-Banach spaces;
Citations & Related Records
연도 인용수 순위
  • Reference
1 T. Aoki, On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan, 2(1950), 64-66.   DOI
2 Y. Benyamini, J. Lindenstrauss, Geometric Nonlinear Functional Analysis, vol. 1. Colloq. Publ. 48(2000), Amer. Math. Soc. Providence.
3 D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Am. Math. Soc., 57(1951), 223-237.   DOI
4 Z. Gajda, On the stability of additive mappings. Int. J. Math. Math. Sci., 14(1991), 431-434.   DOI   ScienceOn
5 Z. X. Gao, H. X. Cao, W. T. Zheng, L. Xu, Generalized Hyers-Ulam-Rassias stability of functional inequalities and functional equations, J. Math. Inequal., 3(2009), 63-77.
6 P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(1994), 431-436.   DOI   ScienceOn
7 D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27(1941), 222-224.   DOI   ScienceOn
8 S. Jung, On the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 204(1996), 221-226.   DOI   ScienceOn
9 H. Kim and E. Son, Hyers-Ulam stability of Jensen Functional Inequality in p-Banach spaces, Abst. and Appl. Anal., 2012, Article ID 270954, 16pp.
10 M. S. Moslehian, A. Najati, An application of a fixed point theorem to a functional inequality, Fixed Point Theory, 10(2009), 141-149.
11 M. Moghimi, A. Najati, C. Park, A functional inequality in restricted domains of Banach modules, Adv. Difference Equations. 2009, Article ID 973709, 14pp.
12 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Am. Math. Soc., 72(1978), 297-300.   DOI   ScienceOn
13 A. Najati, E. G. Zamani, Stability of a mixed additive and cubic functional equation in quasi-Banach spaces, J. Math. Anal. Appl., 342(2008), 1318-1331.   DOI   ScienceOn
14 A. Najati, J. Lee, C. Park, On a Cauchy-Jensen functional inequality, Bull. Malaysian Math. Sci. Soc., 33(2010), 253-263.
15 Th. M. Rassias, The stability of mappings and related topics, in 'Report on the 27th ISFE'. Aequ. Math., 39(1990), 292-293.
16 Th. M. Rassias, P. Semrl, P: On the behaviour of mappings which do not satisfy Hyers-Ulam-Rassias stability, Proc. Am. Math. Soc., 114(1992), 989-993.   DOI   ScienceOn
17 S. M. Ulam, A Collection of the Mathematical Problems. Interscience Publ., New York (1960)
18 J. M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal., 46(1982), 126-130.   DOI
19 J. M. Rassias, On approximation of approximately linear mappings by linear mappings, Bull. Sci. Math., 108(1984), 445-446.
20 S. Rolewicz, Metric Linear Spaces. PWN-Polish Scientific Publishers, Reidel, Warszawa, Dordrecht (1984)
21 A. Najati, 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   ScienceOn