Research Article
Hyers-Ulam-Rassias of Orthogonal Pexiderized Quadratic Functional Equation
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 92 - Issue 9 |
| Published: April 2014 |
| Authors: Iz. El-Fassi, S. Kabbaj |
10.5120/16038-4895
|
Iz. El-Fassi, S. Kabbaj . Hyers-Ulam-Rassias of Orthogonal Pexiderized Quadratic Functional Equation. International Journal of Computer Applications. 92, 9 (April 2014), 20-24. DOI=10.5120/16038-4895
@article{ 10.5120/16038-4895,
author = { Iz. El-Fassi,S. Kabbaj },
title = { Hyers-Ulam-Rassias of Orthogonal Pexiderized Quadratic Functional Equation },
journal = { International Journal of Computer Applications },
year = { 2014 },
volume = { 92 },
number = { 9 },
pages = { 20-24 },
doi = { 10.5120/16038-4895 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2014
%A Iz. El-Fassi
%A S. Kabbaj
%T Hyers-Ulam-Rassias of Orthogonal Pexiderized Quadratic Functional Equation%T
%J International Journal of Computer Applications
%V 92
%N 9
%P 20-24
%R 10.5120/16038-4895
%I Foundation of Computer Science (FCS), NY, USA
Abstract
The Hyers-Ulam-Rassias stability of the conditional quadratic functional equation of Pexider type is established where is a symmetric orthogonality in the sense of Rätz.
References
- J. Aczél, A short course on functional equations, D. Reidel Publ. Co. ,Dordrecht, 1987.
- J. Aczél and J. Dhombres, Functional Equations in Several Vaiables, Cambridge Univ. Press, 1989.
- P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984), 76-86.
- S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64.
- S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scienti?c, River Edge, NJ, 2002.
- S. Czerwik (ed. ), Stability of Functional Equations of Ulam –Hyers–Rassias Type, Hadronic Press, 2003.
- F. Drljevic, On a functional which is quadratic on A- orthogonal vectors. Publ. Inst. Math. (Beograd)(N. S. ) 54(1986), 63-71.
- IZ. EL-Fassi, N. Bounader, A. Chahbi and S. Kabbaj, "On the stability of sigma quadratic functional equation" Jyoti Academic Press, Vol. 2, Issue 2, 2013, Page 61-76, ISSN 2319-6939
- M. Fochi, Functional equations in A-orthogonal vectors, Aequationes Math. 38 (1989), 28-40.
- R. Ger and J. Sikorska, Stability of the orthogonal additivity, Bull Polish Acad. Sci. Math. 43 (1995), No. 2, 143-151.
- D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222224.
- D. H. Hyers, G. Isac and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, 1998. the Absence of the Mountain
- K. W. Jun and Y. H. Lee, On the Hyers–Ulam–Rassias stability of a pexiderized quadratic inequality, Math. Ineq. Appl. , 4(1) (2001), 93118.
- S. -M. Jung and P. Sahoo, Hyers-Ulam stability of the quadratic equation of Pexider type, J. Korean Math. Soc. 38 (2001), No. 3, 645-656.
- M. S. Moslehian, On the stability of the orthogonal Pexiderized Cauchy equation, arXiv math. FA/0412474.
- M. S. Moslehian, On the Orthogonal Stability of the Pexiderized quadratic equation, arXiv: math/0412475v2 [math. FA] 12 Feb 2005.
- Th. M. Rassias, On the stability of the quadratic functional equation and its applications, Studia Univ. Babes-Bolyai Math. 43 (1998), no. 3, 89-124.
- Th. M. Rassias, On the Stability of the Linear mapping in Banach spaces, Procc. Of the Amer. Math. Soc. , (72)(2)(1978), 297-300.
- Th. M. Rassias, On the Stability of the functional equations in Banach spaces, J. Math. Anal. Appl. , (251)(2000), 264-284
- J. Ratz, On orthogonally additive mappings, Aequations Math. 28 (1985),35-49.
- J. Sikorska "Generalized orthogonal stability of some functional equations" Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2006, Article ID 12404, Pages 1–23 DOI 10. 1155/JIA/2006/12404
- F. Skof Local properties and approximations of operators, Rend. Sem. Mat. Fis. Milano 53 (1983) 113-129.
- Gy. Szabo, Sesquilinear-orthogonally quadratic mappings, Aequationes Math. 40 (1990), 190-200.
- S. M. Ulam, A collection of the Mathematical Problem, Interscience Publ. New York, 1960.
- F. Vajzovic, Uber das Funktional H mit der Eigenschaft: (x, y) = 0 ? H(x+y)+H(x?y) = 2H(x)+2H(y), Glasnik Mat. Ser. III 2 (22) (1967), 73-81.
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