Research Article
Hyers-Ulam-Rassias Stability of Quadratic Functional Equations in 2-Banach Spaces
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 63 - Issue 8 |
| Published: February 2013 |
| Authors: Manoj Kumar, Renu Chugh, Ashish |
10.5120/10483-5225
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Manoj Kumar, Renu Chugh, Ashish . Hyers-Ulam-Rassias Stability of Quadratic Functional Equations in 2-Banach Spaces. International Journal of Computer Applications. 63, 8 (February 2013), 1-4. DOI=10.5120/10483-5225
@article{ 10.5120/10483-5225,
author = { Manoj Kumar,Renu Chugh,Ashish },
title = { Hyers-Ulam-Rassias Stability of Quadratic Functional Equations in 2-Banach Spaces },
journal = { International Journal of Computer Applications },
year = { 2013 },
volume = { 63 },
number = { 8 },
pages = { 1-4 },
doi = { 10.5120/10483-5225 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2013
%A Manoj Kumar
%A Renu Chugh
%A Ashish
%T Hyers-Ulam-Rassias Stability of Quadratic Functional Equations in 2-Banach Spaces%T
%J International Journal of Computer Applications
%V 63
%N 8
%P 1-4
%R 10.5120/10483-5225
%I Foundation of Computer Science (FCS), NY, USA
Abstract
In this paper, using the direct method we study the generalized Hyers-Ulam-Rassias stability of the following quadratic functional equations and for the mapping f from normed linear space in to 2-Banach spaces.
References
- A. White, 2-Banach spaces, Doctorial Diss. , St. Louis Univ. , 1968.
- A. White, 2-Banach spaces, Math. Nachr. (42) (1969), pp. 43–60.
- D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. (27) (1941), pp. 222–224.
- H. A. Kenary, D. Y. Shin, J. R. Lee and H. Hoseini, Fixed Point and Hyers-Ulam stability of functional equations, (5) (37) (2011), pp. 1827-1833.
- I. S. Chang and H. M. Kim, On the Hyers-Ulam-Rassias stability of quadratic functional equations, J. Ineq. Pure and Appl. Math. , (3) (3) (2002), pp. 1-12.
- P. Gavruta, A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings, J. Math. Anal. Appl. (184) (1994), pp. 431–436.
- S. G¨ahler, 2-metrische R¨aume und ihre topologische Struktur, Math. Nachr. (26) (1963), pp. 115–148.
- S. G¨ahler, Lineare 2-normierte R¨aumen, Math. Nachr. (28) (1964), pp. 1–43.
- S. G¨ahler, Uber ¨ 2-Banach-R¨aume, Math. Nachr. (42) (1969), pp. 335–347.
- S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. , New York, 1960.
- Th. M. Rassias, On the stability of the Linear mapping in Banach spaces, Procc. of the Amer. Math. Soc. , (72) (2) (1978), pp. 297-300.
- Th. M. Rassias, On the Stability of Functional Equations in Banach spaces, J. Math. Anal. Appl. , (251) (2000), pp. 264–284.
- W. -G. Park, Approximate additive mapping in 2-Banach spaces and related topics, J. Math. Anal. Appl. (376) (2011), pp. 193–202.
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