Some hyperstability results for a Cauchy-Jensen type functional equation in 2-Banach spaces

• Naif Sayar, Khaled Yahya ^[1] ; Bergam, Amal ^[1]
  1. [1] Abdelmalek Essaâdi University

     Abdelmalek Essaâdi University

     Marruecos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 1, 2020, págs. 73-89
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-01-0005
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we investigate some stability and hyperstability results for the following Cauchy-Jensen functional equation in 2-Banach spaces by using Brzdȩk’s fixed point approach.

     

• Referencias bibliográficas
  • M. Almahalebi and C. Park, “On the hyperstability of a functional equation in commutative groups”, Journal of computational analysis and applications,...
  • M. Almahalebi and A. Chahbi, “Hyperstability of the Jensen functional equation in ultrametric spaces”, Aequationes mathematicae, vol. 91,...
  • M. Almahalebi, “Non-Archimedean hyperstability of a Cauchy-Jensen type functional equation”, Journal of classical analysis, vol. 11, no. 2,...
  • T. Aoki, “On the stability of the linear transformation in Banach spaces”, Journal of the mathematical society of Japan, vol. 2, no. 1-2,...
  • L. Aiemsomboon and W. Sintunavarat, “On new stability results for generalized Cauchy functional equations on groups by using Brzdȩk’s fixed...
  • L. Aiemsomboon and W. Sintunavarat, “On generalized hyperstability of a general linear equation”, Acta mathematica hungarica, vol. 149, no....
  • C. Baak, “Cauchy-Rassias stability of Cauchy-Jensen additive mappings in Banach spaces”, Acta mathematica sinica, vol. 22, no. 6, pp. 1789-1796,...
  • D. G. Bourgin, “Classes of transformations and bordering transformations”, Bulletin of the American mathematical society, vol. 57, no. 4,...
  • J. Brzdȩk, “A note on stability of additive mappings,” in Stability of mappings of Hyers-Ulam type, T. M. Rassias and J. Tabor, Eds. Palm...
  • J. Brzdȩk and K. Ciepliński, “A fixed point approach to the stability of functional equations in non-Archimedean metric spaces”, Nonlinear...
  • J. Brzdȩk and K. Ciepliński, “On a fixed point theorm in 2-Banach spaces and some of its applications”, Acta mathematica scientia, vol. 38,...
  • J. Brzdȩk, D. Popa, I. Raşa, B. Xu, Ulam stability of operators, Amsterdam: Academic press, 2018, doi: 10.1016/C2015-0-06292-X.
  • J. Brzdȩk, “Stability of additivity and fixed point methods”, Fixed point theory and applications, Art. ID. 265, 2013, doi: 10.1186/1687-1812-2013-285.
  • J. Brzdȩk, “Hyperstability of the Cauchy equation on restricted domains”, Acta mathematica hungarica, vol. 141, no. 1-2, pp. 58-67, Oct. 2013,...
  • J. Brzdȩk, L. Cadăriu and K. Ciepliński, “Fixed point theory and the Ulam stability”, Journal of function spaces, Art. ID 829419, Aug. 2014,...
  • J. Brzdȩk, W. Fechner, M. S. Moslehian and J. Sikorska, “Recent developments of the conditional stability of the homomorphism equation”, Banach...
  • R. W. Freese and Y. J. Cho, Geometry of linear 2-normed spaces. Hauppauge, NY: Nova Science Publishers, Inc., 2001.
  • D. H. Hyers, “On the stability of the linear functional equation”, Proceedings of the national academy of sciences of the United States of...
  • W. G. Park, “Approximate additive mappings in 2-Banach spaces and related topics”, Journal of mathematical analysis and applications, vol....
  • C. Park, “Fixed points and Hyers-Ulam-Rassias stability of Cauchy Jensen functional equations in Banach algebras”, Fixed point theory and...
  • Th. M. Rassias, “On the stability of the linear mapping in Banach spaces”, Proceedings of the American mathematical society, vol. 72, pp....
  • Th. M. Rassias, “Problem 16, 2°. The Twenty-seventh International Symposium on Functional Equations, August 14–24, 1989, Bielsko-BiałKatowice—Kraków,...
  • Th. M. Rassias, “On a modified Hyers-Ulam sequence”, Journal of mathematical analysis and applications, vol. 158, no. 1, pp. 106-113, Jun....
  • S. M. Ulam, Problems in modern mathematics. New York, NY: John Wiley & Sons, 1964.