We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 December 2024
Reseach Article

Hyers-Ulam-Rassias Stability of Quadratic Functional Equations in 2-Banach Spaces

by Manoj Kumar, Renu Chugh, Ashish
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 63 - Number 8
Year of Publication: 2013
Authors: Manoj Kumar, Renu Chugh, Ashish
10.5120/10483-5225

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 },
issue_date = { February 2013 },
volume = { 63 },
number = { 8 },
month = { February },
year = { 2013 },
issn = { 0975-8887 },
pages = { 1-4 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume63/number8/10483-5225/ },
doi = { 10.5120/10483-5225 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:13:35.075930+05:30
%A Manoj Kumar
%A Renu Chugh
%A Ashish
%T Hyers-Ulam-Rassias Stability of Quadratic Functional Equations in 2-Banach Spaces
%J International Journal of Computer Applications
%@ 0975-8887
%V 63
%N 8
%P 1-4
%D 2013
%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
  1. A. White, 2-Banach spaces, Doctorial Diss. , St. Louis Univ. , 1968.
  2. A. White, 2-Banach spaces, Math. Nachr. (42) (1969), pp. 43–60.
  3. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. (27) (1941), pp. 222–224.
  4. 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.
  5. 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.
  6. P. Gavruta, A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings, J. Math. Anal. Appl. (184) (1994), pp. 431–436.
  7. S. G¨ahler, 2-metrische R¨aume und ihre topologische Struktur, Math. Nachr. (26) (1963), pp. 115–148.
  8. S. G¨ahler, Lineare 2-normierte R¨aumen, Math. Nachr. (28) (1964), pp. 1–43.
  9. S. G¨ahler, Uber ¨ 2-Banach-R¨aume, Math. Nachr. (42) (1969), pp. 335–347.
  10. S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. , New York, 1960.
  11. 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.
  12. Th. M. Rassias, On the Stability of Functional Equations in Banach spaces, J. Math. Anal. Appl. , (251) (2000), pp. 264–284.
  13. W. -G. Park, Approximate additive mapping in 2-Banach spaces and related topics, J. Math. Anal. Appl. (376) (2011), pp. 193–202.
Index Terms

Computer Science
Information Sciences

Keywords

Linear 2-normed space 2-Banach spaces Quadratic functional equations Stability