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Hyers-Ulam-Rassias Stability of Orthogonal Quadratic Functional Equation

by Manoj Kumar, Renu Chugh, Ashish
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 62 - Number 18
Year of Publication: 2013
Authors: Manoj Kumar, Renu Chugh, Ashish
10.5120/10184-5074

Manoj Kumar, Renu Chugh, Ashish . Hyers-Ulam-Rassias Stability of Orthogonal Quadratic Functional Equation. International Journal of Computer Applications. 62, 18 ( January 2013), 42-46. DOI=10.5120/10184-5074

@article{ 10.5120/10184-5074,
author = { Manoj Kumar, Renu Chugh, Ashish },
title = { Hyers-Ulam-Rassias Stability of Orthogonal Quadratic Functional Equation },
journal = { International Journal of Computer Applications },
issue_date = { January 2013 },
volume = { 62 },
number = { 18 },
month = { January },
year = { 2013 },
issn = { 0975-8887 },
pages = { 42-46 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume62/number18/10184-5074/ },
doi = { 10.5120/10184-5074 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:12:12.393838+05:30
%A Manoj Kumar
%A Renu Chugh
%A Ashish
%T Hyers-Ulam-Rassias Stability of Orthogonal Quadratic Functional Equation
%J International Journal of Computer Applications
%@ 0975-8887
%V 62
%N 18
%P 42-46
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we study the Hyers-Ulam-Rassias stability of the quadratic functional equations for the mapping f from orthogonal linear space in to Banach space. Furthermore, we establish the asymptotic behavior of the above quadratic functional equation. The main result has been supported by well constructed example.

References
  1. C. R. Dimmine, R. W. Freese, E. Z. Andalafte, An extension of Pythagorean and isosceles orthogonality and a characterization of inner product spaces, J. Approx. Theory (39)(4)(1983), 295-298.
  2. D. H. Hyers, On the Stability of the Linear Functional Equation, Proc. Nat. Acad. Sci. U. S. A. (27)(1941), 222–224.
  3. F. Drljevic, On a functional which is quadratic on A-orthogonal vectors, publ. Inst. Math. (Beograd), (54)(1986), 63-71.
  4. F. Skof, Local properties and approximations of operators, Rend. Sem. Mat. Fis. Milano, (53)(1983),113-129.
  5. F. Vajzovic, Uber das functional H mit der Eigenschaft: (x, y) = 0 implies H(x+y)+H(x-y) = 2H(x)+2H(y), Glasnik Mat. Ser. III, (22)(1967), 73-81.
  6. G. Birkhoff, Orthogonality in linear metric spaces, Duke Math. J. , (1)(1995), 169-172.
  7. Gy. Szabo, Sesqulinear-orthogonally quadratic mappings, Aequationes Math. , (40)(1990), 190-200.
  8. J. Ratz, On orthogonality additive mappings, Aeq. Math. (28)(1985), 35-49.
  9. K. Sundaresan, Orthogonality and nonlinear functional on Banach spaces, Proc. Amer. Math. Soc. , (34)(1972), 187-190
  10. M. S. Moslehian, On the stability of the orthogonal Pexiderized Cauchy equation, J. Math. Anl. Appl. , (318)(1)(2006), 211-223.
  11. M. S. Moslehian, On the Orthogonal Stability of the Pexiderized Quadratic Equation, J. Difference Equ. Appl. , (11)(2005), 999–1004.
  12. M. Fochi, Functional equations in A-orthogonal vectors, Aequationes Math. , (38)(1989), 28-40.
  13. M. Mirzavaziri, M, S, Moslehian, A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc. , (37)(3)(2006), 361-376.
  14. O. P. Kapoor, J. Prasad, Orthogonality and Characterizations of inner product spaces, Bull. Austral. Math. Soc. , (19)(3)(1978), 403-416.
  15. P. W. Cholewa, Remarks on the stability of functional equations, Aequations Math. (27)(1984), 76-86.
  16. P. Gavruta, A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings, J. Math. Anal. Appl. (184)(1994), 431–436.
  17. R. C. James, Orthogonality in normed linear spaces, Duke Math. J. , (12)(1945), 291-302.
  18. R. Chugh and Ashish, On the stability of generalized Cauchy linear functional equations, Int. J. of Math. Anal. , (6)(29)(2012), 1403 – 1413.
  19. R. Ger and J. Sikorska, Stability of the orthogonal additivity , Bull. Polish Acad. Sci. Math. , (43)(1995),143-151.
  20. S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960.
  21. S. Gudder and D. Strawther, Orthogonality additive and Orthogonality increasing functions on vector spaces, Pacific J. Math. , (58)(1975), 427-436.
  22. T. Aoki, On the stability of the linear transformation in Banach spaces, J. of Math. Soc. , (2)(1-2)(1950), 64-66.
  23. Th. M. Rassias, On the stability of the Linear mapping in Banach spaces, Procc. of the Amer. Math. Soc. , (72)(2)(1978), 297-300.
  24. Th. M. Rassias, On the Stability of Functional Equations in Banach spaces, J. Math. Anal. Appl. , (251)(2000), 264–284.
  25. W. Towanlong, p. Nakmahachalasiant, A quadratic functional equation and its generalized Hyers-Ulam-Rassias stability, Thai j. of Math. , Special Issue (Annual meeting in Mathematics), (2008), 85-91.
Index Terms

Computer Science
Information Sciences

Keywords

Hyers-Ulam-Rassias stability Orthogonal spaces Quadratic functional equations

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