논문KCI 등재
Fixed points and stability of an AQCQ-functional equation in $G$-normed spaces
한국수학교육학회|2016.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제23권 제3호|pp. 265-285
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In this paper, we introduce functional equations in $G$-normed spaces and we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in complete $G$-normed spaces by using the fixed point method.
Abstract
In this paper, we introduce functional equations in $G$-normed spaces and we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in complete $G$-normed spaces by using the fixed point method.
참고문헌 (44)
- J. Aczel, "Functional Equations in Several Variables" (1989), Cambridge Univ. Press
- T. Aoki, "On the stability of the linear transformation in Banach spaces", J. Math. Soc. Japan, 2, pp.64~66 (1950)
- D.G. Bourgin, "Classes of transformations and bordering transformations", Bull. Amer. Math. Soc, 57, pp.223~237 (1951)
- L. C. adariu, "Fixed points and the stability of Jensen's functional equation", J. Inequal. Pure Appl. Math, 4(1) (2003)
- L. C. adariu, "On the stability of the Cauchy functional equation: a ¯xed point approach", Grazer Math. Ber, 346, pp.43~52 (2004)
- L. C. adariu, "Fixed point methods for the generalized stability of functional equations in a single variable", Fixed Point Theory and Applications (2008)
- Y. Cho, "Functional inequalities in non-Archimedean Banach spaces", Appl. Math. Letters, 23, pp.1238~1242 (2010)
- P.W. Cholewa, "Remarks on the stability of functional equations", Aequationes Math, 27, pp.76~86 (1984)
- C.-Y. Chou, "On approximate isomorphisms between Banach *-algebras or C¤-algebras", Taiwanese J. Math, 10, pp.219~231 (2006)
- S. Czerwik, "On the stability of the quadratic mapping in normed spaces", Abh. Math. Sem. Univ. Hamburg, 62, pp.59~64 (1992)
- P. Czerwik, "Functional Equations and Inequalities in Several Variables" (2002), World Scientic Publishing Company
- J. Diaz, "A xed point theorem of the alternative for contractions on a generalized complete metric space", Bull. Amer. Math. Soc, 74, pp.305~309 (1968)
- M. Eshaghi Gordji, "On the stability of a generalized qua-dratic and quartic type functional equation in quasi-Banach spaces", J. Inequal. Appl (2009)
- M. Eshaghi Gordji, "Stability of an additive-cubic-quartic functional equation", Advances in Di®erence Equations (2009)
- G.L. Forti, "Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations", J. Math. Anal. Appl, 295, pp.127~133 (2004)
- G.L. Forti, "Elementary remarks on Ulam-Hyers stability of linear functional equations", J. Math. Anal. Appl, 328, pp.109~118 (2007)
- P. Gavruta, "A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings", J. Math. Anal. Appl, 184, pp.431~436 (1994)
- D.H. Hyers, "On the stability of the linear functional equation", Proc. Nat. Acad. Sci. U.S.A, 27, pp.222~224 (1941)
- D.H. Hyers, "Stability of Functional Equations in Several Variables" (1998), BirkhÄauser
- G. Isac, "Stability of Ã-additive mappings: Appications to nonlinear analysis", Internat. J. Math. Math. Sci, 19, pp.219~228 (1996)
- K. Jun, "The generalized Hyers-Ulam-Rassias stability of a cubic functional equation", J. Math. Anal. Appl, 274, pp.867~878 (2002)
- K. Jun, "Approximate derivations mapping into the radicals of Banach algebras", Tai-wanese J. Math, 11, pp.277~288 (2007)
- S. Jung, "Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Anal-ysis" (2001), Hadronic Press lnc
- J. Lee, "A xed point approach to the stability of an additive-quadratic-cubic-quartic functional equation", Fixed Point Theory and Applications (2010)
- S. Lee, "Quartic functional equations", J. Math. Anal. Appl, 307, pp.387~394 (2005)
- D. Mihet, "On the stability of the additive Cauchy functional equation in random normed spaces", J. Math. Anal. Appl, 343, pp.567~572 (2008)
- M. Mirzavaziri, "A xed point approach to stability of a quadratic equation", Bull. Braz. Math. Soc, 37, pp.361~376 (2006)
- M.S. Moslehian, "Jensen's functional equations in multi-normed spaces", Taiwanese J. Math, 14, pp.453~462 (2010)
- Z. Mustafa, "A new approach to generalized metric spaces", J. Nonlinear Convex Anal, 7, pp.289~297 (2006)
- C. Park, "Linear functional equations in Banach modules over a C¤-algebra", Acta Appl. Math, 77, pp.125~161 (2003)
- C. Park, "Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras", Fixed Point Theory and Applications (2007)
- C. Park, "Generalized Hyers-Ulam-Rassias stability of quadratic functional equations:a xed point approach", Fixed Point Theory and Applications (2008)
- C. Park, "Fixed points and the stability of an AQCQ-functional equation in non-Archimedean normed spaces", Abstract and Applied Analysis (2010)
- 박춘길, "ON THE STABILITY OF AN AQCQ-FUNCTIONAL EQUATION", 충청수학회지, 22(4), pp.757~770 (2009), 충청수학회
- C. Park, "Hyers-Ulam stability of functional equations in G-normed spaces", ~
- V. Radu, "The xed point alternative and the stability of functional equations", Fixed Point Theory, 4, pp.91~96 (2003)
- M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
- M. Rassias, "On the stability of functional equations in Banach spaces", J. Math. Anal. Appl, 251, pp.264~284 (2000)
- M. Rassias, "On the stability of functional equations and a problem of Ulam", Acta Appl. Math, 62, pp.23~130 (2000)
- M. Rassias, "On the behaviour of mappings which do not satisfy Hyers-Ulam stability", Proc. Amer. Math. Soc, 114, pp.989~993 (1992)
- M. Rassias, "On the Hyers-Ulam stability of linear mappings", J. Math. Anal. Appl, 173, pp.325~338 (1993)
- R. Saadati, "Non-Archimedean L-fuzzy normed spaces and stability of func-tional equations", Computers Math. Appl, 60, pp.2488~2496 (2010)
- F. Skof, "Proprietµa locali e approssimazione di operatori", Rend. Sem. Mat. Fis. Milano, 53, pp.113~129 (1983)
- S.M. Ulam, "A Collection of the Mathematical Problems" (1960), Interscience Publ
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