논문KCI 등재
Stability of the Jensen type functional equation in Banach algebras: a fixed point approach
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
주제분류수학
초록
Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the following Jensen type functional equation:f[수식]+f[수식]=f(x).
Abstract
Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the following Jensen type functional equation:f[수식]+f[수식]=f(x).
참고문헌 (30)
- C. Baak, "Cauchy-Rassias stability of Cauchy-Jensen additive mappings in Banach spaces", Acta Math. Sin, 22, pp.1789~1796 (2006)
- C. Baak, "Generalized additive mapping in Banach modules and isomorphisms between C*-algebras", J. Math. Anal. Appl, 314, pp.150~161 (2006)
- L. Cadariu, "Fixed points and the stability of Jensen's functional equation", J. Inequal. Pure Appl. Math, 4(1) (2003)
- P.W. Cholewa, "Remarks on the stability of functional equations", Aequationes Math, 27, pp.76~86 (1984)
- S. Czerwik, "On the stability of the quadratic mapping in normed spaces", Abh. Math. Sem. Univ. Hamburg, 62, pp.59~64 (1992)
- 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)
- 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. Natl. Acad. Sci. U.S.A, 27, pp.222~224 (1941)
- D.H. Hyers, "Topics in Nonlinear Analysis and Applications" (1997), World Scientic Publishing Co., Singapore, New Jersey, London
- D.H. Hyers, "Stability of Functional Equations in Several Variables" (1998), Birkhauser, Basel
- F.H. Hyers, "Approximate homomorphisms", Aequationes Math, 44, pp.125~153 (1992)
- G. Isac, "Stability of -additive mappings: appications to nonlinear analysis", Internat. J. Math. Math. Sci, 19, pp.219~228 (1996)
- 정순모, "Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis" (2001), Hadronic Press, Inc.
- C. Park, "Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras", Fixed Point Theory Appl, ~ (2007), Art. ID 50175
- Chun-Gil Park, "Homomorphisms between $C^*$-algebras associated with the Triffunctional equation and linear derivations on$C^*$-algebras", 대한수학회지, 41(3), pp.461~477 (2004), 대한수학회
- C. Park, "Homomorphisms between JC-algebras and between Lie C-algebras", Acta Math. Sin, 21, pp.1391~1398 (2005)
- 박춘길, "On a Generalized Trif's Mapping in Banach Modules over a$C^*$-Algebra", 대한수학회지, 43(2), pp.323~356 (2006), 대한수학회
- J.M. Rassias, "On approximation of approximately linear mappings by linear mappings", Bull. Sci. Math, 108, pp.445~446 (1984)
- J.M. Rassias, "Solution of a problem of Ulam", J. Approx. Theory, 57, pp.268~273 (1989)
- Th.M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
- Th.M. Rassias, "On modied Hyers-Ulam sequence", J. Math. Anal. Appl, 158, pp.106~113 (1991)
- Th.M. Rassias, "On the stability of the quadratic functional equation and its applications", Studia Univ. Babes-Bolyai, Ser. Math, XLIII, pp.89~124 (1998)
- Th.M. Rassias, "The problem of S.M. Ulam for approximately multiplicative mappings", J. Math. Anal. Appl, 246, pp.352~378 (2000)
- Th.M. Rassias, "On the stability of functional equations in Banach spaces", J. Math. Anal. Appl, 251, pp.264~284 (2000)
- Th.M. Rassias, "On the stability of functional equations and a problem of Ulam", Acta Appl. Math, 62, pp.23~130 (2000)
- Th.M. Rassias, "On the behavior of mappings which do not satisfy Hyers-Ulam stability", Proc. Amer. Math. Soc, 114, pp.989~993 (1992)
- Th.M. Rassias, "On the Hyers-Ulam stability of linear mappings", J. Math. Anal. Appl, 173, pp.325~338 (1993)
- Th.M. Rassias, "Variational problem of some quadratic functionals in complex analysis", J. Math. Anal. Appl, 228, pp.234~253 (1998)
- F. Skof, "Proprieta locali e approssimazione di operatori", Rend. Sem. Mat. Fis. Milano, 53, pp.113~129 (1983)
- S.M. Ulam, "Problems in Modern Mathematics" (1960), Wiley, New York
관련 논문AI추천
Stability of the Cauchy functional equation in Banach algebras박춘길, 이정례강원경기수학회 · 한국수학논문집2009 · 제17권 제1호Stability of the Jensen functional equation in fuzzy Banach algebras신동윤, 이정례강원경기수학회 · 한국수학논문집2012 · 제20권 제1호A FIXED POINT APPROACH TO THE CAUCHY-RASSIAS STABILITY OF GENERAL JENSEN TYPE QUADRATIC-QUADRATIC MAPPINGS박춘길, H. Khodaei, M. Eshaghi Gordji대한수학회 · 대한수학회보2010 · 제47권 제5호Fuzzy algebra homomorphisms and fuzzy derivations이정례강원경기수학회 · 한국수학논문집2014 · 제22권 제4호Hyers-Ulam Stability of Jensen Functional Equation in p- Banach Spaces김학만, 손은영, 전길웅경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제3호A Fixed Point Approach to the Stability of 3-Lie Homomorphisms and 3-Lie Derivations이정례, Siriluk Paokanta한국수학교육학회 · 이론수학과 교직수학2019 · 제26권 제4호
이 간행물의 다른 논문 (10건)
Tricomi problem for the elliptic-hyperbolic equation of the second kindM.S. Salahitdinov, N.K. Mamadalievpp. 111-127The Zeta-determinants of Harmonic Oscillators on R^2김경화pp. 129-147Almost splitting sets S of an integral domain D such that D_S is a PID장규환pp. 163-169On the Superstability of the generalized Sine Functional Equations김광휘, 한미현pp. 171-180Subgroup actions and some applications박상원, 한준철pp. 181-189
