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Year 2024, Volume: 14 Issue: 2, 144 - 159, 31.07.2024

Abstract

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

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.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematics Education, Science Education, Science and Mathematics Education (Other)
Journal Section Research Article
Authors

Abderrahman Baza This is me

Mohamed Rossafi

Publication Date July 31, 2024
Published in Issue Year 2024 Volume: 14 Issue: 2

Cite

APA Baza, A., & Rossafi, M. (2024). Stability of Radical Cubic Functional Inequality in Modular Spaces and Fuzzy Banach Space. Azerbaijan Journal of Mathematics, 14(2), 144-159.
AMA Baza A, Rossafi M. Stability of Radical Cubic Functional Inequality in Modular Spaces and Fuzzy Banach Space. AZJM. July 2024;14(2):144-159.
Chicago Baza, Abderrahman, and Mohamed Rossafi. “Stability of Radical Cubic Functional Inequality in Modular Spaces and Fuzzy Banach Space”. Azerbaijan Journal of Mathematics 14, no. 2 (July 2024): 144-59.
EndNote Baza A, Rossafi M (July 1, 2024) Stability of Radical Cubic Functional Inequality in Modular Spaces and Fuzzy Banach Space. Azerbaijan Journal of Mathematics 14 2 144–159.
IEEE A. Baza and M. Rossafi, “Stability of Radical Cubic Functional Inequality in Modular Spaces and Fuzzy Banach Space”, AZJM, vol. 14, no. 2, pp. 144–159, 2024.
ISNAD Baza, Abderrahman - Rossafi, Mohamed. “Stability of Radical Cubic Functional Inequality in Modular Spaces and Fuzzy Banach Space”. Azerbaijan Journal of Mathematics 14/2 (July 2024), 144-159.
JAMA Baza A, Rossafi M. Stability of Radical Cubic Functional Inequality in Modular Spaces and Fuzzy Banach Space. AZJM. 2024;14:144–159.
MLA Baza, Abderrahman and Mohamed Rossafi. “Stability of Radical Cubic Functional Inequality in Modular Spaces and Fuzzy Banach Space”. Azerbaijan Journal of Mathematics, vol. 14, no. 2, 2024, pp. 144-59.
Vancouver Baza A, Rossafi M. Stability of Radical Cubic Functional Inequality in Modular Spaces and Fuzzy Banach Space. AZJM. 2024;14(2):144-59.