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Reseach Article

On the Stability of Functional Equations in Random Normed Spaces

by Renu Chugh, Ashish
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 45 - Number 11
Year of Publication: 2012
Authors: Renu Chugh, Ashish
10.5120/6825-9353

Renu Chugh, Ashish . On the Stability of Functional Equations in Random Normed Spaces. International Journal of Computer Applications. 45, 11 ( May 2012), 25-34. DOI=10.5120/6825-9353

@article{ 10.5120/6825-9353,
author = { Renu Chugh, Ashish },
title = { On the Stability of Functional Equations in Random Normed Spaces },
journal = { International Journal of Computer Applications },
issue_date = { May 2012 },
volume = { 45 },
number = { 11 },
month = { May },
year = { 2012 },
issn = { 0975-8887 },
pages = { 25-34 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume45/number11/6825-9353/ },
doi = { 10.5120/6825-9353 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:37:22.620465+05:30
%A Renu Chugh
%A Ashish
%T On the Stability of Functional Equations in Random Normed Spaces
%J International Journal of Computer Applications
%@ 0975-8887
%V 45
%N 11
%P 25-34
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Let f be a mapping from a linear space X into a complete Random Normed Space Y. In this paper, we prove some results for the stability of Cubic, Quadratic and Jensen-Type Quadratic functional equations in the setting of Random Normed Spaces (RNS).

References
  1. A. Wiwatwanich and P. Nakmahachalasint : On the stability of a Cubic Functional Equation, Thai Journal of Mathematics, Special Issue (Annual Meeting in Mathematics, 2008) : 69-76.
  2. A. N. Sherstnev : On the notion of a random normed space. Dpkl. Akad. Nauk SSSR 149,280-283(1963) (in Russian).
  3. B. Schweizer and A. Sklar : Prpbabilistic Metric Spaces. North-Holland, New York(1983).
  4. C. Alsina, B. Schweizer and A. Sklar : On the definition of a probabilistic normed space. equ. Math. 46, 91-98(1993)
  5. C. Park : On the Stability of the Linear Mapping in Banach Modules, J. Math. Anal. Appl. , 275 (2002), 711–720.
  6. C. Park and Th. M. Rassias : Isometric Additive Mappings in Generalized Quasi-Banach spaces, Banach J. Math. Anal. , 2 (2008), 59–69.
  7. D. H. Hyers : On the Stability of the Linear Functional Equation, Proc. Nat. Acad. Sci. U. S. A. 27(1941), 222–224.
  8. D. H. Hyers and Th. M. Rassias : Approximate Homomorphisms, Aequationes Math. , 44 (1992), 125–153.
  9. D. H. Hyers : On the stability of the Linear Functional Equation, Procc. of the National Academy of science of the U. S. A. , 27(1941), pp. 867-878.
  10. E. Baktash, Y. J. Cho, M. Jalili, R. Saadati and S. M. Vaezpour: On the Stability of Cubic Mapping and Quadratic Mapping in Random Normed Spaces, Journal of Inequalities and Appl. , Vol. 2008,Article ID 902187, 11 pages.
  11. F. Skof : Local properties and approximations of operators, Rend. Sem. Mat. Fis. Milano, 53(1983) 113-129.
  12. I. -S. Chang, Jun, K. -W. and Y. S. Jung : The modified Hyers – Ulam – Rassias stability of a cubic type functional equation, Math. Inequal. Appl. 8(4)(2005) pp. 675683.
  13. I. -S. Chang and Y. S. Jung : Stability of functional equation deriving from cubic and quadratic functions, Journal of Mathematical Analysis and Appl. 282(2003) 491-500
  14. K. W. Jun and H. M. Kim : The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, J. Anal. Appl. 274(2) (2002) pp. 867-878.
  15. K. H. Park and Y. S. Jung : Stability of a cubic functional equation on qroups, Bulletin of the Korean Mathematical Society, vol. 41,no. 2,pp. 347-357,2004.
  16. M. S. Moslehian : On the Orthogonal Stability of the Pexiderized Quadratic Equation, J. Difference Equ. Appl. , 11 (2005), 999–1004.
  17. P. W. Cholewa : Remarks on the stability of functional equations, Aequations Math. 27(1984) 76-86.
  18. P. Gavruta : A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings, J. Math. Anal. Appl. 184 (1994), 431–436.
  19. S. M. Ulam : A Collection of the Mathematical Problems, Interscience Publ. New York, 1960.
  20. S. M. Ulam : Problems on Modern Mathematics, John Wiley and Sons, New York, NY, USA, 1964.
  21. S. Czerwik : Functional Equations and Inequalities in Several Variables, World Scienti?c Publ. Co. , New Jersey, London, Singapore and Hong Kong, 2002.
  22. S. Czerwik : Stability of Functional Equations of Ulam-Hyers-Rassias Type, Hadronic Press Inc. , Palm Harbor, Florida, 2003.
  23. S. Jung,: Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press Inc. , Palm Harbor, Florida, 2001.
  24. S. Y. Jang, Rye Lee, C. Park and Dong Yun Shin : Fuzzy stability of Jensen – Type Quadratic functional equations, Abstract and Applied Analysis, vol. 2009,Article ID 535678.
  25. Th. M. Rassias : On the stability of the Linear mapping in Banach spaces, Procc. Of the American Mathematical Society, vol. 72, no. 2, pp. 297-300,1978.
  26. Th. M. Rassias : Problem 16; 2, Report of the 27th International Symp. on Functional Equations, Aequationes Math. , 39 (1990), 292–293; 309.
  27. Th. M. Rassias : On the Stability of Functional Equations in Banach spaces, J. Math. Anal. Appl. , 251 (2000), 264–284.
  28. T. Aoki: On the stability of the linear transformation in Banach spaces, Journal of the Mathematical Society, vol. 2, no. 1-2, pp. 64-66,1950.
Index Terms

Computer Science
Information Sciences

Keywords

Quadratic Functional Equation Cubic Functional Equation Jensen-type Quadratic Functional Equation Hyers-ulam-rassias Stability Random Normed Spaces