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http://dx.doi.org/10.5666/KMJ.2013.53.3.419

A General System of Nonlinear Functional Equations in Non-Archimedean Spaces  

Ghaemi, Mohammad Bagher (Department of Mathematics, Iran University of Science and Technology)
Majani, Hamid (Department of Mathematics, Iran University of Science and Technology)
Gordji, Madjid Eshaghi (Department of Mathematics, Semnan University)
Publication Information
Kyungpook Mathematical Journal / v.53, no.3, 2013 , pp. 419-433 More about this Journal
Abstract
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.
Keywords
Nonlinear Functional Equations; non-Archimedean Normed spaces; Generalized Hyers-Ulam-Rassias stability;
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Times Cited By KSCI : 6  (Citation Analysis)
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1 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.   DOI   ScienceOn
2 P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(1994), 431-436.   DOI   ScienceOn
3 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.   과학기술학회마을   DOI   ScienceOn
4 O. Hadzic, A fixed point theorem in Menger spaces, Publ. Inst. Math. (Beograd), T20(1979), 107-112.
5 O. Hadzic, Fixed point theorems for multivalued mappings in probabilistic metric spaces, Fuzzy Sets Syst., 88(1997), 219-226.   DOI   ScienceOn
6 D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27(1941), 222-224.   DOI   ScienceOn
7 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.   과학기술학회마을
8 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.   과학기술학회마을   DOI   ScienceOn
9 A. K. Katsaras and A. Beoyiannis, Tensor products of non-Archimedean weighted spaces of continuous functions, Georgian Mathematical Journal, 6(1999), 33-44.   DOI   ScienceOn
10 A. Khrennikov, non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer Academic Publishers, Dordrecht, 1997.
11 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.
12 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.
13 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.   DOI   ScienceOn
14 M. Eshaghi Gordji and H. Khodaei, Stability of Functional Equations, LAP LAMBERT Academic Publishing, 2010.
15 D. Mihet, The stability of the additive Cauchy functional equationin non-Archimedean fuzzy normed spaces, Fuzzy Sets Syst., 161(2010), 2206-2212.   DOI   ScienceOn
16 A. K. Mirmostafaee, Hyers-Ulam Stability of Cubic Mappings in non-Archimedean Normed Spaces, Kyungpook Math. J., 50(2010), 315-327.   과학기술학회마을   DOI   ScienceOn
17 A. K. Mirmostafaee, M. S. Moslehian, Stability of additive mappings in non- Archimedean fuzzy normed spaces, Fuzzy Sets Syst., 160(2009), 1643-1652.   DOI   ScienceOn
18 L. Narici, E. Beckenstein, Strange terrain-non-Archimedean spaces, Amer. Math. Mon., 88(9)(1981) 667-676.   DOI   ScienceOn
19 C. Alsina, B. Schweizer and A. Sklar, On the definition of a probabilistic normed space, Aequationes Math., 46(1993), 91-98.   DOI   ScienceOn
20 T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2(1950), 64-66.   DOI
21 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.   DOI
22 C. Baak and M. S. Moslehian, On the Stability of Orthogonally Cubic Functional Equations , Kyungpook Math. J., 47(2007), 69-76.   과학기술학회마을
23 D. Deses, On the representation of non-Archimedean objects, Topology and its Applications, 153(2005), 774-785.   DOI   ScienceOn
24 P. J. Nyikos, On some non-Archimedean spaces of Alexandrof and Urysohn, Topology and its Applications, 91(1991), 1-23.
25 C. Park, D. H. Boo and Th. M. Rassias, Approximately addtive mappings over p-adic fields, J. Chungcheong Math. Soc., 21(2008), 1-14.
26 B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland, NewYork, 1983.
27 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.   DOI
28 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.   과학기술학회마을   DOI   ScienceOn
29 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72(1978), 297-300.   DOI   ScienceOn
30 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.
31 S. M. Ulam, Problems in Modern Mathematics, Chapter VI, Science Editions, Wiley, New York, 1964.
32 V. S. Vladimirov, I. V. Volovich and E. I. Zelenov, p-adic Analysis and Mathematical Physics, World Scientific, 1994.