General solution and hyperstability results for a cubic radical functional equation related to quadratic mapping

• El Ghali, Rachid ^[1] ; Almahalebi, Muaadh ^[1] ; Kabbaj, Samir ^[1]
  1. [1] Université Ibn-Tofail

     Université Ibn-Tofail

     Kenitra, Marruecos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 1, 2020, págs. 107-122
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-01-0007
• Enlaces
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• Resumen

  • The aim of this paper is to introduce and solve the following radical cubic functional equation Also, we investigate some stability results for the considered equation in Banach spaces.

• Referencias bibliográficas
  • [1] L. Aiemsomboon and W. Sintunavarat, “On generalized hyperstability of a general linear equation”, Acta mathematica hungarica, vol. 149,...
  • [2] M. Almahalebi, A. Charifi and S. Kabbaj, “Hyperstability of a Cauchy functional equation”, Journal of nonlinear analysis and optimization:...
  • [3] T. Aoki, “On the stability of the linear transformation in Banach spaces”, Journal of the mathematical society of Japan, vol. 2, no. 1-2,...
  • [4] D. G. Bourgin, “Classes of transformations and bordering transformations”, Bulletin of the American mathematical society, vol. 57, no....
  • [5] J. Brzdęk and J. Tabor, “A note on stability of additive mappings”, in Stability of mappings of Hyers-Ulam type, T. M. Rassias, Ed. Palm...
  • [6] J. Brzdęk, J. Chudziak, and Z. Páles, “A fixed point approach to stability of functional equations”, Nonlinear analysis: theory, methods...
  • [7] J. Brzdęk, Hyperstability of the Cauchy equation on restricted domains, Acta mathematica hungarica, vol. 141, no. 1-2, pp. 58-67, Oct....
  • [8] J. Brzdęk, “Remark 3. 16th International Conference on Functional Equations and Inequalities, Będlewo, Poland, May 17-23, 2015”, Annales...
  • [9] M. Eshaghi Gordji, H. Khodaei, A. Ebadian, and G. H. Kim, “Nearly radical quadratic functional equations in p-2-normed spaces”, Abstract...
  • [10] D. H. Hyers, “On the stability of the linear functional equation”, Proceedings of the National Academy of Sciences of the United States...
  • [11] H. Khodaei, M. Eshaghi Gordji, S. S. Kim, and Y. J. Cho, “Approximation of radical functional equations related to quadratic and quartic...
  • [12] S. S. Kim, Y. J. Cho and M. Eshaghi Gordji, “On the generalized Hyers-Ulam-Rassias stability problem of radical functional equations”,...
  • [13] G. Maksa and Z. Pales, “Hyperstability of a class of linear functional equations”, Acta mathematica academiae paedagogicae nyiregyhaziensis,...
  • [14] Th. M. Rassias, “On the stability of the linear mapping in Banach spaces”, Proceeding of the American mathematical society, vol. 72,...
  • [15] Th. M. Rassias, “Problem 16, 2°. The Twenty-seventh International Symposium on Functional Equations, August 14–24, 1989, Bielsko-BiałKatowice—Kraków,...
  • [16] Th. M. Rassias, “On a modified Hyers-Ulam sequence”, Journal of mathematical analysis and applications, vol. 158, no. 1, pp. 106-113,...
  • [17] S. M. Ulam, Problems in modern mathematics. New York, NY: John Wiley & Sons, 1964.