Browse > Article
http://dx.doi.org/10.14317/jami.2020.415

UNIQUENESS THEOREM CONCERNING FUNCTIONAL EQUATIONS IN MODULAR SPACES  

JEON, YOUNGJU (Department of Mathematics Education, College of Education, Jeonbuk National University)
KIM, CHANGIL (Department of Mathematics Education, Dankook University)
Publication Information
Journal of applied mathematics & informatics / v.38, no.5_6, 2020 , pp. 415-426 More about this Journal
Abstract
In this paper, we will prove some uniqueness theorems that can be applied to the generalized Hyers-Ulam stability of some additive-quadratic-cubic functional equation in complete modular spaces without Δ2-conditions.
Keywords
Fixed point theorem; stability; modular spaces;
Citations & Related Records
연도 인용수 순위
  • Reference
1 T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64-66.   DOI
2 P. Gavruta, A generalization of the Hyer-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436.   DOI
3 D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. 27 (1941), 222-224.   DOI
4 M.A. Khamsi, Quasicontraction mappings in modular spaces without ${\Delta}_2$-condition, Fixed Point Theory and Applications 2008 (2008), 1-6.   DOI
5 S. Koshi and T. Shimogaki, On F-norms of quasi-modular spaces, J. Fac. Sci. Hokkaido Univ. Ser. 15 (1961), 202-218.   DOI
6 M. Krbec, Modular interpolation spaces I, Z. Anal. Anwendungen 1 (1982), 25-40.   DOI
7 Y.H. Lee, S.M. Jung, and M.Th. Rassias, Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation, Journal of Mathematical Inequalities 12 (2018), 43-61.   DOI
8 A. Luxemburg, Banach function spaces, Ph.D. Thesis, Technische Hogeschool te Delft, Netherlands, 1959.
9 J. Musielak and W. Orlicz, On modular spaces, Studia Math. 18 (1959), 49-65.   DOI
10 L. Maligranda, Orlicz Spaces and Interpolation, Seminars in Math. Vol. 5, Univ. Estadual de Campinas, Campinas SP, 1989.
11 J. Musielak, Orlicz Spaces and Modular Spaces, Springer-verlag, Berlin, 1983.
12 H. Nakano, Modular semi-ordered linear spaces, Tokyo, Japan, 1959.
13 Th.M. Rassias, On the stability of the linear mapping in Banach sapces, Proc. Amer. Math. Sco. 72 (1978), 297-300.   DOI
14 M.A. Khamsi, W.M. Kozowski and S. Reich, Fixed point theory in modular function spaces, Nonlinear Anal. 14 (1990), 935-953.   DOI
15 G. Sadeghi, A fixed point approach to stability of functional equations in modular spaces, Bull. Malays. Math. Sci. Soc. 37 (2014), 333-344.
16 Ph. Turpin, Fubini inequalities and bounded multiplier property in generalized modular spaces, Comment. Math. 1 (1978), 331-353.
17 S.M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1960(Chapter VI).
18 S. Yamamuro, On conjugate spaces of Nakano spaces, Trans. Amer. Math. Soc. 90 (1959), 291-311.   DOI
19 K. Wongkum, P. Chaipunya, and P. Kumam, On the generalized Ulam-Hyers-Rassias stability of quadratic mappings in modular spaces without 42-conditions, Journal of function spaces 2015 (2015), 1-6.