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A General System of Nonlinear Functional Equations in Non-Archimedean Spaces
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  • Journal title : Kyungpook mathematical journal
  • Volume 53, Issue 3,  2013, pp.419-433
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2013.53.3.419
 Title & Authors
A General System of Nonlinear Functional Equations in Non-Archimedean Spaces
Ghaemi, Mohammad Bagher; Majani, Hamid; Gordji, Madjid Eshaghi;
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In this paper, we prove the generalized Hyers-Ulam-Rassias stability for a system of functional equations, called general system of nonlinear functional equations, in non-Archimedean normed spaces and Menger probabilistic non-Archimedean normed spaces.
Nonlinear Functional Equations;non-Archimedean Normed spaces;Generalized Hyers-Ulam-Rassias stability;
 Cited by
C. Alsina, B. Schweizer and A. Sklar, On the definition of a probabilistic normed space, Aequationes Math., 46(1993), 91-98. crossref(new window)

T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2(1950), 64-66. crossref(new window)

L. M. Arriola and W. A. Beyer, Stability of the Cauchy functional equation over p-adic fields, Real Anal. Exchange, 31(2005/2006), 125-132. crossref(new window)

C. Baak and M. S. Moslehian, On the Stability of Orthogonally Cubic Functional Equations , Kyungpook Math. J., 47(2007), 69-76.

D. Deses, On the representation of non-Archimedean objects, Topology and its Applications, 153(2005), 774-785. crossref(new window)

M. Eshaghi Gordji, M. B. Ghaemi and H. Majani, Generalized Hyers-Ulam-Rassias Theorem in Menger Probabilistic Normed Spaces, Discrete Dynamics in Nature and Society, Volume 2010, Article ID 162371, 11 pages.

M. Eshaghi Gordji, M. B. Ghaemi, H. Majani and C. Park, Generalized Ulam-Hyers Stability of Jensen Functional Equation in Serstnev PN Spaces, Journal of Inequalities and Applications, Volume 2010, Article ID 868193, 14 pages.

M. Eshaghi Gordji, H. Khodaei, Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi-Banach spaces, Nonlinear Anal., 71(2009), 5629-5643. crossref(new window)

M. Eshaghi Gordji and H. Khodaei, Stability of Functional Equations, LAP LAMBERT Academic Publishing, 2010.

M. Eshaghi Gordji and M. B. Savadkouhi, Stability of a mixed type cubic-quartic functional equation in non-Archimedean spaces, Appl. Math. Lett.' 23(10)(2010), 1198-1202. crossref(new window)

P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(1994), 431-436. crossref(new window)

M. B. Ghaemi, H. Majani and M. Eshaghi Gordji, Approximately Quintic And Sextic Mappings On The Probabilistic Normed Spaces, Bull. Korean Math. Soc., 49(2)(2012), 339-352. crossref(new window)

O. Hadzic, A fixed point theorem in Menger spaces, Publ. Inst. Math. (Beograd), T20(1979), 107-112.

O. Hadzic, Fixed point theorems for multivalued mappings in probabilistic metric spaces, Fuzzy Sets Syst., 88(1997), 219-226. crossref(new window)

D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27(1941), 222-224. crossref(new window)

K.-W. Jun and Y.-H. Lee, A Generalization of the Hyers-Ulam-Rassias Stability of the Pexiderized Quadratic Equations, II, Kyungpook Math. J., 47(2007), 91-103.

Y.-S. Jung and K.-H. Park, On the Generalized Hyers-Ulam-Rassias Stability for a Functional Equation of Two Types in p-Banach Spaces, Kyungpook Math. J., 48(2008), 45-61. crossref(new window)

A. K. Katsaras and A. Beoyiannis, Tensor products of non-Archimedean weighted spaces of continuous functions, Georgian Mathematical Journal, 6(1999), 33-44. crossref(new window)

A. Khrennikov, non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer Academic Publishers, Dordrecht, 1997.

D. Mihet, The stability of the additive Cauchy functional equationin non-Archimedean fuzzy normed spaces, Fuzzy Sets Syst., 161(2010), 2206-2212. crossref(new window)

A. K. Mirmostafaee, Hyers-Ulam Stability of Cubic Mappings in non-Archimedean Normed Spaces, Kyungpook Math. J., 50(2010), 315-327. crossref(new window)

A. K. Mirmostafaee, M. S. Moslehian, Stability of additive mappings in non- Archimedean fuzzy normed spaces, Fuzzy Sets Syst., 160(2009), 1643-1652. crossref(new window)

L. Narici, E. Beckenstein, Strange terrain-non-Archimedean spaces, Amer. Math. Mon., 88(9)(1981) 667-676. crossref(new window)

P. J. Nyikos, On some non-Archimedean spaces of Alexandrof and Urysohn, Topology and its Applications, 91(1991), 1-23.

C. Park, D. H. Boo and Th. M. Rassias, Approximately addtive mappings over p-adic fields, J. Chungcheong Math. Soc., 21(2008), 1-14.

C. Park, M. Eshaghi Gordji, M. B. Ghaemi and H. Majani, Fixed points and approximately octic mappings in non-Archimedean 2-normed spaces, J. Ineq. Appl., 2012, 2012: 289 doi:10.1186/1029-242X-2012-289. crossref(new window)

K.-H. Park and Y.-S. Jung, On the Generalized Hyers-Ulam-Rassias Stability of Higher Ring Derivations , Kyungpook Math. J., 49(2009), 67-79. crossref(new window)

Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72(1978), 297-300. crossref(new window)

B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland, NewYork, 1983.

A. N. Serstnev, On the motion of a random normed space, Dokl. Akad. Nauk SSSR, 149(1963), 280-283, English translation in Soviet Math. Dokl., 4(1963), 388-390.

S. M. Ulam, Problems in Modern Mathematics, Chapter VI, Science Editions, Wiley, New York, 1964.

V. S. Vladimirov, I. V. Volovich and E. I. Zelenov, p-adic Analysis and Mathematical Physics, World Scientific, 1994.