Year 2024,
Volume: 14 Issue: 2, 144 - 159, 31.07.2024
Abderrahman Baza
Mohamed Rossafi
References
- [1] I. Amemiya, On the representation of complemented modular lattices, J.
Math. Soc. Japan, 9(2), 1957, 263–279.
- [2] Y. Aribou, S. Kabbaj, New functional inequality in non-Archimedean Banach
spaces related to radical cubic functional equation, Asia Math., 2(3), 2018,
24–31.
- [3] T. Bag, S.K. Samanta, Finite dimensional fuzzy normed linear space, J.
Fuzzy Math., 11(2), 2003, 687–706.
- [4] J.A. Baker, The stability of certain functional equations, Proc. Am. Math.
Soc., 112(3), 1991, 729–732.
- [5] L. Cadariu, V. Radu, Fixed Points and the Stability of Jensen’s Functional
Equation, J. Inequalities Pure Appl., 4(4), 2003, 1–7.
- [6] Y.J. Cho, C. Park, R. Saadati, Functional inequalities in non-Archimedean
Banach spaces, Appl. Math. Lett., 23(10), 2010, 1238–1242.
- [7] J.B. Diaz, B. Margolis, A Fixed Point Theorem of the Alternative, for Contractions on a Generalized Complete Metric Space, Bull. Am. Math. Soc.,
74(2), 1968, 305–309.
- [8] P. Gavruja, A generalization of the hyers-ulam-rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(3), 1994, 431–436.
- [9] D.H. Hyers, On the Stability of the Linear Functional Equation, Proc. Natl.
Acad. Sci., 27(4), 1941, 222–224.
- [10] M.A. Khamsi, Quasicontraction mappings in modular spaces without ∆2-
condition, Fixed Point Theory Appl., 2008, 2008, 1-6.
- [11] S. Koshi, T. Shimogaki, on F-Norms of Quasi-Modular Spaces, J. Fac. Sci.,
Hokkaido Univ., Ser. 1 , 15(3–4), 1961.
- [12] M. Krbec, Modular Interpolation Spaces I, Zeitschrift F¨ur Anal. Und Ihre
Anwendungen, 1(1), 1982, 25–40.
- [13] W.A. Luxemburg, Banach function spaces, PhD Thesis, Delft University of
Technology, Delft, The Netherlands, 1959.
- [14] B. Mazur, Modular curves and the eisenstein ideal, Publ. Math´ematiques
L’Institut Des Hautes Sci., 47(1), 1977, 33–186.
- [15] D. Mihet, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl., 343, 2008, 567-572.
- [16] J. Musielak, Orlicz Spaces and Modular Spaces, Lect. Notes Math. 1034
Springer, Berlin, Germany, 1983.
- [17] H. Nakano, Modulared Semi-Ordered Linear Spaces, Maruzen, Tokyo, Japan,
1950.
- [18] W. Orlicz, Collected Papers, I, II, PWN, Warszawa, 1988.
- [19] Z. P´ales, Generalized stability of the Cauchy functional equation, Aequationes Math., 56(3), 1998, 222–232.
Stability of Radical Cubic Functional Inequality in Modular Spaces and Fuzzy Banach Space
Year 2024,
Volume: 14 Issue: 2, 144 - 159, 31.07.2024
Abderrahman Baza
Mohamed Rossafi
Abstract
The aim of this paper is to investigate the Hyers-Ulam stability of radical
cubic functional inequality in modular space with ∆2-condition and in fuzzy Banach
space
References
- [1] I. Amemiya, On the representation of complemented modular lattices, J.
Math. Soc. Japan, 9(2), 1957, 263–279.
- [2] Y. Aribou, S. Kabbaj, New functional inequality in non-Archimedean Banach
spaces related to radical cubic functional equation, Asia Math., 2(3), 2018,
24–31.
- [3] T. Bag, S.K. Samanta, Finite dimensional fuzzy normed linear space, J.
Fuzzy Math., 11(2), 2003, 687–706.
- [4] J.A. Baker, The stability of certain functional equations, Proc. Am. Math.
Soc., 112(3), 1991, 729–732.
- [5] L. Cadariu, V. Radu, Fixed Points and the Stability of Jensen’s Functional
Equation, J. Inequalities Pure Appl., 4(4), 2003, 1–7.
- [6] Y.J. Cho, C. Park, R. Saadati, Functional inequalities in non-Archimedean
Banach spaces, Appl. Math. Lett., 23(10), 2010, 1238–1242.
- [7] J.B. Diaz, B. Margolis, A Fixed Point Theorem of the Alternative, for Contractions on a Generalized Complete Metric Space, Bull. Am. Math. Soc.,
74(2), 1968, 305–309.
- [8] P. Gavruja, A generalization of the hyers-ulam-rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(3), 1994, 431–436.
- [9] D.H. Hyers, On the Stability of the Linear Functional Equation, Proc. Natl.
Acad. Sci., 27(4), 1941, 222–224.
- [10] M.A. Khamsi, Quasicontraction mappings in modular spaces without ∆2-
condition, Fixed Point Theory Appl., 2008, 2008, 1-6.
- [11] S. Koshi, T. Shimogaki, on F-Norms of Quasi-Modular Spaces, J. Fac. Sci.,
Hokkaido Univ., Ser. 1 , 15(3–4), 1961.
- [12] M. Krbec, Modular Interpolation Spaces I, Zeitschrift F¨ur Anal. Und Ihre
Anwendungen, 1(1), 1982, 25–40.
- [13] W.A. Luxemburg, Banach function spaces, PhD Thesis, Delft University of
Technology, Delft, The Netherlands, 1959.
- [14] B. Mazur, Modular curves and the eisenstein ideal, Publ. Math´ematiques
L’Institut Des Hautes Sci., 47(1), 1977, 33–186.
- [15] D. Mihet, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl., 343, 2008, 567-572.
- [16] J. Musielak, Orlicz Spaces and Modular Spaces, Lect. Notes Math. 1034
Springer, Berlin, Germany, 1983.
- [17] H. Nakano, Modulared Semi-Ordered Linear Spaces, Maruzen, Tokyo, Japan,
1950.
- [18] W. Orlicz, Collected Papers, I, II, PWN, Warszawa, 1988.
- [19] Z. P´ales, Generalized stability of the Cauchy functional equation, Aequationes Math., 56(3), 1998, 222–232.