Ulam Stability Generalizations of 4th- Order Ternary Derivations Associated to a Jmrassias Quartic Functional Equation on Fréchet Algebras

• Journal title : Kyungpook mathematical journal
• Volume 53, Issue 2,  2013, pp.233-245
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2013.53.2.233
Title & Authors
Ulam Stability Generalizations of 4th- Order Ternary Derivations Associated to a Jmrassias Quartic Functional Equation on Fréchet Algebras

Abstract
Let $\small{\mathcal{A}}$ be a Banach ternary algebra over a scalar field R or C and $\small{\mathcal{X}}$ be a ternary Banach $\small{\mathcal{A}}$-module. A quartic mapping $\small{D\;:\;(\mathcal{A},[\;]_{\mathcal{A}}){\rightarrow}(\mathcal{X},[\;]_{\mathcal{X}})}$ is called a $\small{4^{th}}$- order ternary derivation if $D([x,y,z]) Keywords Ulam stability;Quartic functional equation;Fr$\small{\acute{e}}$chet algebras;Ternary Banach algebras;$\small{4^{th}}$- order ternary derivation; Language English Cited by References 1. V. Abramov, R. Kerner and B. Le Roy, Hypersymmetry a Z3 graded generalization of supersymmetry, J. Math. Phys., 38(1997), 1650. 2. J. Aczel, J. Dhombres, Functional equations in several variables, Cambridge Univ. Press., 1989. 3. M. Bavand Savadkouhi, M. Eshaghi Gordji, J. M. Rassias and N. Ghobadipour, Approximate ternary Jordan derivations on Banac ternary algebras, J. Math. Phys., 50(2009), 9 pages. 4. N. Bazunova, A. Borowiec and R. Kerner, Universal differential calculus on ternary algebras, Lett. Math. Phys., 67(2004). 5. A. Cayley, On the 34 concomitants of the ternary cubic, Amer. J. Math., 4(1881), 1-15. 6. P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math., 27(1984), 76-86. 7. H. Chu, S. Koo and J. Park, Partial stabilities and partial derivations of n-variable functions, Nonlinear Anal.-TMA (to appear). 8. J. K. Chung, P. K. Sahoo, On the general solution of a quartic functional equation, Bull. Korean Math. Soc., 40(2003), 565-?76. 9. S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg, 62(1992), 59-64. 10. A. Ebadian, A. Najati and M. Eshaghi Gordji, On approximate additive-quartic and quadratic-cubic functional equations in two variables on abelian groups, Results Math., 58(2010), 39-53. 11. A. Ebadian, N. Ghobadipour and M. Eshaghi Gordji, A fixed point method for perturbation of bimultipliers and Jordan bimultipliers in C*-ternary algebras, Journal of mathematical physics, 51(2010), 103508. 12. A. Ebadian, N. Ghobadipour, M. Banand Savadkouhi and M. Eshaghi Gordji, Stability of a mixed type cubic and quartic functional equation in non-Archimedean$\ell$-fuzzy normed spaces, Thai Journal of Mathematic,9(2)(2011), 225-241. 13. A. Ebadian, N. Ghobadipour, Th. M. Rassias and M. Eshaghi Gordji, Functional Inequalities Associated with Cauchy Additive Functional Equation in Non-Archimedean Spaces, To appear in Discrete Dynamics in Nature and Society. 14. A. Ebadian, N. Ghobadipour, Th. M. Rassias and I. Nikoufar, Stability of generalized derivations on Hilbert C* - modules associated to a pexiderized Cuachy-Jensen type functional equation, To appear in Acta Mathematica Scintia. 15. M. Eshaghi Gordji, A. Ebadian and S. Zolfaghari, Stability of a functional equation deriving from cubic and quartic functions, Abs. Appl. Anal., 2008, Article ID 801904, 17 pages. 16. M. Eshaghi Gordji, Stability of an additive-quadratic functional equation of two variables in Fpaces, Journal of Nonlinear Sciences and Applications, 2(2009), 251-259. 17. M. Eshaghi Gordji, N. Ghobadipour, Nearly generalized Jordan derivations, Math. Slovaca, 61(1)(2011), 1-8. 18. M. Eshaghi Gordgi, N. Ghobadipour, Approximately quartic homomorphisms on Banach algebras, Word applied sciences Journal, (2010), Article in press. 19. M. Eshaghi Gordji, N. Ghobadipour, Stability of ($\alpha$,$\beta$,$\gamma$)-derivations on Lie C*-algebras, International Journal of Geometric Methods in Modern Physics, 7(2010), 1093-1102. 20. M. Eshaghi Gordji, J. M. Rassias and N. Ghobadipour, Generalized Hyers-Ulam stability of the generalized (n, k)-derivations, Abs. Appl. Anal., 2009, Article ID 437931, 8 pages. 21. Z. Gajda, On stability of additive mappings, Internat. J. Math. Sci. 14(1991), 431-434. 22. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(1994), 431-436. 23. P. Gavruta, An answer to a question of Th.M. Rassias and J. Tabor on mixed stability of mappings, Bul. Stiint. Univ. Politeh. Timis. Ser. Mat. Fiz., 4(56)(1997), 1-6. 24. P. Gavruta, On the Hyers-Ulam-Rassias stability of mappings, in: Recent Progress in Inequalities, 430, Kluwer, 1998, 465-469. 25. Ghobadipour, N.,Lie * - double derivations on Lie C* -algebras, Int. J. Nonlinear Anal. Appl. 1 (2010) No.2, 1-12. 26. N. Ghobadipour, A. Ebadian, Th. M. Rassias and M. Eshaghi, A perturbation of double derivations on Banach algebras, Communications in Mathematical Analysis, 11(2011), 51-60. 27. D. H. Hyers, G. Isac and Th. M. Rassias, Stability of functional equations in several variables, Birkhaer, Basel. (1998). 28. D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27(1941), 222-224. 29. G. Isac, Th. M. Rassias, On the Hyers-Ulam stability of$\psi\$-additive mappings, J. Approx. Theory, 72(1993), 131-137.

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