STABILITY OF EULER-LAGRANGE QUADRATIC FUNCTIONAL EQUATIONS IN NON-ARCHIMEDEAN NORMED SPACES

Yıl 2011, Cilt: 40 Sayı: 4, 571 - 579, 01.04.2011

Ghadir Sadeghi Reza Saadati M. Janfada J.m. Rassias

Öz

In this paper, we prove the stability of Euler-Lagrange quadratic mappings in the framework of non-Archimedean normed spaces. Our results
in the setting of non-Archimedean normed spaces are different from the
results in the setting of normed spaces.

Anahtar Kelimeler

Generalized Hyers-Ulam stability, Euler-Lagrange functional equation, Non-Archimedean normed space, p-adic field, 2000 AMS Classification: Primary 39B22, Secondary 39B82, 46S10

Kaynakça

• Arriola, L. M. and Beyer, W. A. Stability of the Cauchy functional equation over p-adic fields, Real Anal. Exchange 31, 125–132, 2005/2006.
• Cho, Y. J., Park, C. and Saadati, R. Functional inequalities in non-Archimedean Banach spaces, Appl. Math. Letters 10, 1238–1242, 2010.
• Czerwik, S. Stability of Functional Equations of Ulam-Hyers-Rassias Type (Hadronic Press, Palm Harbor, Florida, 2003).
• Forti, G. L. Hyers-Ulam stability of functional equations in several variables Aequationes Math. 50, 143–190, 1995.
• Hyers, D. H. and Rassias, Th. M. Approximate homomorphisms, Aequationes Math. 44, 125–153, 1992.
• Hyers, D. H., Isac, G. and Rassias, Th. M. Stability of Functional Equations in Several Variables(Birkh¨auser, Basel, 1998).
• Jun, K. and Kim, H. The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, J. Math. Anal. Appl. 274, 867–878, 2002.
• Jung, S. Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis (Hadronic Press lnc., Palm Harbor, Florida, 2001).
• Lee, Y. and Chung, S. Stability of an Euler-Lagrange-Rassias equation in the spaces of generalized functions, Appl. Math. Letters 21, 694–700, 2008.
• Kim, H. and Rassias, J. M. Generalization of Ulam stability problem for Euler-Lagrange quadratic mappings, J. Math. Anal. Appl. 336, 277–296, 2007.
• Moslehian, M. S. The Jensen functional equation in non-Archimedian normed spaces, J. Funct. Spaces. Appl. 2 (1), 13–24, 2009.
• Moslehian, M. S. and Rassias, Th. M. Stability of functional equations in non-Archimedian spaces, Appl. Anal. Disc. Math. 2, 325–334, 2007.
• Moslehian, M. S. and Sadeghi, Gh. Stability of tow type of cubic functional equations in non-Archimedian spaces, Real. Anal. Exchange 33, 375–383, 2008.
• Rassias, J. M. On the stability of the non-linear Euler-Lagrange functional equation in real normed linear spaces, J. Math. Phys. Sci. 28, 231–235, 1994.
• Rassias, J. M. On the stability of the general Euler-Lagrange functional equation, Demon- stratio Math. 29, 755–766, 1996.
• Rassias, J. M. Solution of the Ulam stability problem for Euler-Lagrange quadratic mapping, J. Math. Anal. Appl. 220, 613–639, 1998.
• Rassias, J. M. On the stability of the multi-dimensional Euler-Lagrange functional equation, J. Indian Math. Soc. 66, 1–9, 1999.
• Rassias J. M. and Rassias, M. J. Refined Ulam stability for Euler-Lagrange type mappings in Hilbert spaces, Intern. J. Appl. Math. Stat. 7, 126–132, 2007.
• Rassias, Th. M. On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62, 23–130, 2000.
• Rassias, Th. M. Functional Equations, Inequalities and Applications (Kluwer Academic Pub- lishers, Dordrecht, Boston and London, 2003).