Generalized Hyers-Ulam Stability of a General Mixed Additive-cubic Functional Equation in Quasi-Banach Spaces 被引量：3

Generalized Hyers-Ulam Stability of a General Mixed Additive-cubic Functional Equation in Quasi-Banach Spaces

导出

摘要 In this paper, we establish a general solution and the generalized Hyers-Ulam-Rassias stability of the following general mixed additive-cubic functional equation In this paper, we establish a general solution and the generalized Hyers-Ulam-Rassias stability of the following general mixed additive-cubic functional equation

作者 Tian Zhou XU John Michael RASSIAS Wan Xin XU

机构地区 School of Mathematics Pedagogical Department E.E. Department of Electrical and Computer Engineering

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第3期529-560,共32页 数学学报（英文版）

基金 supported by National Natural Science Foundation of China (Grant Nos. 10671013 and11171022)

关键词 Stability additive mapping cubic mapping quasi-Banach space p-Banach space Stability, additive mapping, cubic mapping, quasi-Banach space, p-Banach space

分类号 O177.2 [理学—基础数学] TM911.41 [电气工程—电力电子与电力传动]

引文网络
相关文献

参考文献2

1Dong Seung KANG,Hahng-Yun CHU.Stability Problem of Hyers-Ulam-Rassias for Generalized Forms of Cubic Functional Equation[J].Acta Mathematica Sinica,English Series,2008,24(3):491-502. 被引量：4
2Li Guang WANG Bo LIU.The Hyers-Ulam Stability of a Functional Equation Deriving from Quadratic and Cubic Functions in Quasi-β-normed Spaces[J].Acta Mathematica Sinica,English Series,2010,26(12):2335-2348. 被引量：7

二级参考文献19

1Ulam, S. M.: Problems in Morden Mathematics, Wiley, New York, 1960
2Hyers, D. H.: On the stability of the linear equation. Proc. Nat. Acad. Sci. U.S.A., 27, 222-224 (1941)
3Rassias, Th. M.: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc., 72, 297-300 (1978)
4Gajda, Z.: On the stability of additive mappings. Internat. J. Math. Math. Sci., 14, 431-434 (1991)
5Gavruta, P.: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl., 184, 431-436 (1994)
6Skof, F.: Proprieta locali e approssimazione di operatori. Rend. Semin. Mat. Fis. Milano, 53, 113-129 (1983)
7Cholewa, P. W.: Remarks on the stability of functional equations. Aequationes. Math., 27, 76-86 (1984)
8Czerwik, S.: On the stability of the quadratic mapping in normed spaces. Abh. Math. Sere. Univ. Hamburg, 62, 59-64 (1992)
9Jung, S. M.: On an Asymptotic Behavior of Exponential Functional equation. Acta Mathematica Sinica, English Series, 22(2), 583-586 (2006)
10Rassias, Th. M.: On the stability of functional equations in Banach spaces. J. Math. Anal. Appl., 251, 264-284 (2000)

共引文献9

1Jae-Young CHUNG.Stability of a Generalized Quadratic Functional Equation in Schwartz Distributions[J].Acta Mathematica Sinica,English Series,2009,25(9):1459-1468. 被引量：1
2Ick-Soon CHANG,Eunyoung SON,Hark-Mahn KIM.Refined Functional Equations Stemming from Cubic,Quadratic and Additive Mappings[J].Acta Mathematica Sinica,English Series,2009,25(10):1595-1608. 被引量：1
3Jaiok ROH,Yong-Soo JUNG,Ick-Soon CHANG.A Note on the Stability of Jordan Triple Higher Ring Derivations[J].Acta Mathematica Sinica,English Series,2009,25(12):1975-1986.
4John Michael RASSIAS,Kil Woung,JUN Hark-Mahn KIM.Approximate （m, n）-Cauchy-Jensen Additive Mappings in C^＊-algebras[J].Acta Mathematica Sinica,English Series,2011,27(10):1907-1922.
5王利广,刘博.一类源自可加、二次、三次和四次映射的泛函方程的模糊稳定性[J].数学学报（中文版）,2012,55(5):841-854.
6王利广,李静.一类可加和二次混合泛函方程的稳定性[J].数学学报（中文版）,2013,56(4):583-596.
7Li Guang WANG,Kun Peng XU,Qiu Wen LIU.On the Stability of a Mixed Functional Equation Deriving from Additive, Quadratic and Cubic Mappings[J].Acta Mathematica Sinica,English Series,2014,30(6):1033-1049. 被引量：1
8孟庆.迹和中心值迹的稳定性（英文）[J].南开大学学报（自然科学版）,2016,49(4):22-28.
9刘建华,孟庆.锥巴拿赫空间上(α,β)-导子的稳定性[J].南开大学学报（自然科学版）,2020,53(1):41-47.

同被引文献2

1Li Guang WANG Bo LIU.The Hyers-Ulam Stability of a Functional Equation Deriving from Quadratic and Cubic Functions in Quasi-β-normed Spaces[J].Acta Mathematica Sinica,English Series,2010,26(12):2335-2348. 被引量：7
2Janusz BRZDEK,Krzysztof CIEPLINSKI.ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS[J].Acta Mathematica Scientia,2018,38(2):377-390. 被引量：5

引证文献3

1许天周,Rassias John Michael,许婉欣.A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES[J].Acta Mathematica Scientia,2012,32(3):866-892.
2Li Guang WANG,Kun Peng XU,Qiu Wen LIU.On the Stability of a Mixed Functional Equation Deriving from Additive, Quadratic and Cubic Mappings[J].Acta Mathematica Sinica,English Series,2014,30(6):1033-1049. 被引量：1
3Ravinder Kumar SHARMA,Sumit CHANDOK.THE GENERALIZED HYPERSTABILITY OF GENERAL LINEAR EQUATION IN QUASI-2-BANACH SPACE[J].Acta Mathematica Scientia,2022,42(4):1357-1372.

二级引证文献1

1薛文萍,纪培胜.混合AQC函数方程在FFNLS上的HUR稳定性[J].山东大学学报（理学版）,2016,51(4):1-8.

1Pei Sheng JI,Shu Juan ZHOU,Hai Yan XUE.On a Jensen-cubic Functional Equation and Its Hyers-Ulam Stability[J].Acta Mathematica Sinica,English Series,2015,31(12):1929-1940. 被引量：1
2Weimin Wang,Yuqiang Feng,Anli Zheng.ON THE HYERS-ULAM STABILITY OF A THIRD-ORDER NONLINEAR DIFFERENTIAL EQUATION[J].Annals of Applied Mathematics,2015,31(4):437-445.
3玉强,郭艳平.一般四次方程的稳定性(英文)[J].四川师范大学学报（自然科学版）,2013,36(5):703-707. 被引量：8
4纪培胜,占小静,刘荣荣.Banach代数上双导子的Hyers-Ulam-Rassias稳定性[J].东北师大学报（自然科学版）,2013,45(4):12-16. 被引量：1
5郭艳平,曹怀信.拟Banach代数上拟同态的Hyers-Ulam-Rassias稳定性(Ⅰ)[J].纺织高校基础科学学报,2008,21(4):421-424. 被引量：6
6谭磊.线性迭代系统的Hyers-Ulam-Rassias稳定[J].乐山师范学院学报,2015,30(4):6-9.
7Anna BAHYRYCZ,Krzysztof CIEPLINSKI,Jolanta OLKO.ON AN EQUATION CHARACTERIZING MULTI-CAUCHY-JENSEN MAPPINGS AND ITS HYERS-ULAM STABILITY[J].Acta Mathematica Scientia,2015,35(6):1349-1358.
8A.Vinodkumar,K.Malar,M.Gowrisankar,P.Mohankumar.EXISTENCE, UNIQUENESS AND STABILITY OF RANDOM IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS[J].Acta Mathematica Scientia,2016,36(2):428-442. 被引量：4
9Wen YUAN.Complex interpolation and Calderon product of quasi-Banach spaces[J].Frontiers of Mathematics in China,2016,11(3):753-762.
10Dong Seung KANG,Hahng-Yun CHU.Stability Problem of Hyers-Ulam-Rassias for Generalized Forms of Cubic Functional Equation[J].Acta Mathematica Sinica,English Series,2008,24(3):491-502. 被引量：4

Acta Mathematica Sinica,English Series

2012年第3期

浏览历史

内容加载中请稍等...