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 November 2024
Call for Paper
December Edition
IJCA solicits high quality original research papers for the upcoming December edition of the journal. The last date of research paper submission is 20 November 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

Stability of Functional Equations in Multi-Banach Spaces via Fixed Point Approach

by Manoj Kumar, Ashish
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 44 - Number 7
Year of Publication: 2012
Authors: Manoj Kumar, Ashish
10.5120/6278-8445

Manoj Kumar, Ashish . Stability of Functional Equations in Multi-Banach Spaces via Fixed Point Approach. International Journal of Computer Applications. 44, 7 ( April 2012), 35-40. DOI=10.5120/6278-8445

@article{ 10.5120/6278-8445,
author = { Manoj Kumar, Ashish },
title = { Stability of Functional Equations in Multi-Banach Spaces via Fixed Point Approach },
journal = { International Journal of Computer Applications },
issue_date = { April 2012 },
volume = { 44 },
number = { 7 },
month = { April },
year = { 2012 },
issn = { 0975-8887 },
pages = { 35-40 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume44/number7/6278-8445/ },
doi = { 10.5120/6278-8445 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:34:57.367854+05:30
%A Manoj Kumar
%A Ashish
%T Stability of Functional Equations in Multi-Banach Spaces via Fixed Point Approach
%J International Journal of Computer Applications
%@ 0975-8887
%V 44
%N 7
%P 35-40
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, using the fixed point approach, we proved the Hyers-Ulam-Rassias stability of a Jensen-type quadratic functional equations f(ax±ay)-a2[f(x)+f(y)] and f((x±y)/2)-f(x)-f(y)in Multi-Banach Spaces using the ideas from Dales and Polyakov [4].

References
  1. C. Borelli and G. L. Forti, On a general Hyers-Ulam stability, Int. J. Math. Math. Sci. (18)(1995), pp. 229-236.
  2. D. H. Hyers, On the Stability of the Linear Functional Equation, Proc. Nat. Acad. Sci. U. S. A. (27)(1941), pp. 222–224.
  3. F. Skof, Proprietà locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano, (53)(1983), pp. 113–129.
  4. H. G. Dales and M. E. Polyakov, Multi-normed spaces and multi-Banach algebras, preprint.
  5. H. G. Dales and M. S. Moslehian, Stability of mappings on multi- normed spaces, Glasgow Mathematical Journal, (49)(2)(2007), pp. 321– 332.
  6. J. B. Diaz and B. Margolis, A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bulletin of the American Mathematical Society, (74)(1968), pp. 305–309.
  7. L. Wang, B. Liu and R. Bai, Stability of a Mixed Type Functional Equation on Multi-Banach Spaces: A Fixed Point Approach, Fixed Point Theory and Applications, vol. 2010, Art. ID 283827, 9 pages
  8. M. S. Moslehian, Superstability of higher derivations in multi-Banach algebras, Tamsui Oxford Journal of Mathematical Sciences, (24)(4) (2008), pp. 417–427.
  9. M. S. Moslehian, K. Nikodem, and D. Popa, Asymptotic aspect of the quadratic functional equation in multi-normed spaces, Journal of Mathematical Analysis and Applications, (355)(2)(2009), pp. 717– 724.
  10. M. S. Moslehian and H. M. Srivastava, Jensens functional equations in multi-normed spaces, Taiwnese J. of Math. , (14)(2)(2010), pp. 453-462.
  11. O. Had?zi´c, E. Pap, and V. Radu, Generalized contraction mapping principles in probabilistic metric spaces, Acta Mathematica Hungarica, (101)(1-2)(2003), pp. 131–148.
  12. P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. , (27)(1984), pp. 76–86.
  13. P. Gavruta, A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings, J. Math. Anal. Appl. (184)(1994), pp. 431–436.
  14. 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
  15. S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960.
  16. S. Czerwik, On the stability of the quadratic mappings in normed spaces, Abh. Math. Sem. Univ. Hamburg, (62)(1992), pp. 59–64.
  17. Th. M. Rassias, On the stability of the Linear mapping in Banach spaces, Procc. Of the American Mathematical Society, (72)(2)(1978), pp. 297-300.
  18. Th. M. Rassias, On the stability of the functional equations in Banach spaces, J. Math. Anal. Appl. , (251)(2000), pp. 264–284.
  19. T. Aoki, On the stability of the linear transformation in Banach spaces, Journal of the Mathematical Society, (2)(1-2)(1950), pp. 64-66.
  20. V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory, (4)(1)(2003), pp. 91–96.
  21. Z. Wang, X. Li, and Th. M. Rassias, Stability of an Additive-Cubic- Quartic Functional Equation in Multi-Banach Spaces, Abstract and Applied Analysis, vol. 2011, Article ID 536520, 11 pages
Index Terms

Computer Science
Information Sciences

Keywords

Fixed Point Alternative Jensen-type Quadratic Functional Equations Multi-banach Spaces

Powered by PhDFocusTM