논문KCI 등재
ON THE FUZZY STABILITY OF CUBIC MAPPINGS USING FIXED POINT METHOD
한국수학교육학회|2012.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제19권 제4호|pp. 397-407
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
Let X and Y be vector spaces. We introduce a new type of a cubic functional equation f : X → Y . Furthermore, we assume X is a vector space and (Y, N) is a fuzzy Banach space and then investigate a fuzzy version of the generalized Hyers-Ulam stability in fuzzy Banach space by using fixed point method for the cubic functional equation.
Abstract
Let X and Y be vector spaces. We introduce a new type of a cubic functional equation f : X → Y . Furthermore, we assume X is a vector space and (Y, N) is a fuzzy Banach space and then investigate a fuzzy version of the generalized Hyers-Ulam stability in fuzzy Banach space by using fixed point method for the cubic functional equation.
참고문헌 (28)
- T. Aoki, "On the stability of the linear transformation in Banach spaces", J. Math. Soc. Japan, 2, pp.64~66 (1950)
- J.-H. Bae, "On the generalized Hyers-Ulam-Rassias stability in Banach modules over a C¤¡algebra", J. Math. Anal. Appl, 294, pp.196~205 (2004)
- T. Bag, "Finite dimensional fuzzy normed linear spaces", J. Fuzzy Math, 11(3), pp.687~705 (2003)
- L. C¸adariu, "On the stability of the Cauchy functional equation: a fixed point approach", Iteration theory (ECIT '02), pp.346~ (2004), Karl-Franzens- Univ
- L. Cadariu, "Fixed point methods for the generalized stability of functional equations in a single variable", Fixed Point Theory and Applications, 2008 (2008)
- S.C. Cheng, "Fuzzy linear operator and fuzzy normed linear spaces", Bull. Calcutta Math. Soc, 86, pp.429~436 (1994)
- S. Czerwik, "On the stability of the quadratic mapping in normed spaces", Abh. Math. Sem. Univ. Hamburg, 62, pp.59~64 (1992)
- C. Felbin, "Finite dimensional fuzzy normed linear spaces", Fuzzy Sets and Systems, 48(2), pp.239~248 (1992)
- Z. Gajda, "On the stability of additive mappings", Internat. J. Math. Math. Sci, 14, pp.431~434 (1991)
- D.H. Hyers, "On the stability of the linear equation", Proc. Nat. Acad. Sci. U.S.A, 27, pp.222~224 (1941)
- D.H. Hyers, "Approximate homomorphisms", Aequationes Mathematicae, 44, pp.125~153 (1992)
- G. Isac, "Stability of ¼-additive mappings: Applications to nonlinear analysis", Internat. J. Math. Math. Sci, 19(2), pp.219~228 (1996)
- K.-W. Jun, "On the Hyers-Ulam stability of an Euler-Lagrange type cubic functional equation", J. Computatioal analysis and app, 7(1), pp.21~33 (2005)
- A.K. Katsaras, "Fuzzy topological vector spaces II", Fuzzy Sets Sys, 12, pp.143~154 (1984)
- I. Kramosil, "Fuzzy metric and statistical metric spaces", Kybernetica, 11, pp.326~334 (1975)
- S.V. Krishna, "Separation of fuzzy normed linear spaces", Fuzzy Sets and Systems, 63(2), pp.207~217 (1994)
- B. Margolis, "A fixed point theorem of the alternative for contractions on a generalized complete metric space", Bull. Amer. Math. Soc, 126(74), pp.305~309 (1968)
- D. Mihett, "On the stability of the additive Cauchy functional equation in random normed spaces", J. Math. Anal. Appl, 343(1), pp.567~572 (2008)
- A.K. Mirmostafaee, "Fuzzy stability of the Jensen functional equation", Fuzzy Sets Syst, 159, pp.730~738 (2008)
- M. Mirzavaziri, "A fixed point approach to stability of a quadratic equation", Bull. Braz. Math. Soc, 37(3), pp.361~376 (2006)
- C. Park, "Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras", Fixed Point Theory Appl, 2007 (2007)
- J.M. Rassias, "On approximation of approximately linear mappings by linear mappings", Bulletin des Sciences Mathematiques, 108(4), pp.445~446 (1984)
- Th.M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
- V. Radu, "The fixed point alternative and the stability of functional equations", Fixed Point Theory, 4(1), pp.91~96 (2003)
- I.A. Rus, "Principles and Appications of Fixed Point Theory" (1979), Cluj-Napoca
- S.M. Ulam, "Problems in Morden Mathematics" (1960), Wiley
- C. Wu, "Fuzzy generalization of Klomogoroffs theorem", J. Harbin Inst. Technol, 1, pp.1~7 (1984)
- J.Z. Xiao, "Fuzzy normed spaces of operators and its completeness", Fuzzy Sets and Systems, 133(3), pp.389~399 (2003)
관련 논문AI추천
The Hyers-Ulam Stability of Cubic Functrional Equations in Fuzzy Banach Spaces김창일, 윤용식영남수학회 · East Asian Mathematical Journal2014 · 제30권 제3호Fuzzy stability of a cubic-quartic functional equation: a fixed point approach박춘길, 신동윤, 장선영대한수학회 · 대한수학회보2011 · 제48권 제3호Fuzzy stability of a cubic-quadratic functional equation: a fixed point approach박춘길, 이상협, 이상훈강원경기수학회 · 한국수학논문집2009 · 제17권 제3호FUZZY STABILITY OF QUADRATIC-CUBIC FUNCTIONAL EQUATIONS김창일, 윤용식영남수학회 · East Asian Mathematical Journal2016 · 제32권 제3호Quadratic(ρ1, p2)-functional Equation in Fuzzy Banach Spaces신동윤, Siriluk Paokanta한국수학교육학회 · 이론수학과 교직수학2020 · 제27권 제1호Fuzzy stability of an AQCQ-functional equation in matrix fuzzy normed spaces신동윤, 이정례한국수학교육학회 · 이론수학과 교직수학2016 · 제23권 제3호
이 간행물의 다른 논문 (8건)
SOME EQUIVALENT CONDITIONS FOR CONIC SECTIONS서수정, 송부선, 김동수, 범우인, 양덕주, 강주연, 정지은pp. 315-325THE CURVATURE OF HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD OF QUASI-CONSTANT CURVATURE진대호pp. 327-335AREA OF TRIANGLE IN THE PLANE WITH ALPHA DISTANCE FUNCTION김병학, 고일석, 오채희pp. 337-347GROUPS ACTION ON MEDIAN GRAPHS AND MEDIAN COMPLEXES양도형pp. 349-361NEYMAN-PEARSON THEORY AND ITS APPLICATION TO SHORTFALL RISK IN FINANCE김주홍pp. 363-381
