SciELO - Scientific Electronic Library Online

vol.39 número1Some ideal convergent multiplier sequence spaces using de la Vallee Poussin mean and Zweier operatorWeak convergence and weak compactness in the space of integrable functions with respect to a vector measure índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados




Links relacionados

  • En proceso de indezaciónCitado por Google
  • No hay articulos similaresSimilares en SciELO
  • En proceso de indezaciónSimilares en Google


Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.1 Antofagasta feb. 2020 


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

Rachid El Ghali1 

Muaadh Almahalebi2

Samir Kabbaj3

1 Ibn Tofaïl University, Dept. of Mathematics, Kenitra, Morocco. e-mail:

2 Ibn Tofaïl University, Dept. of Mathematics, Kenitra, Morocco e-mail:

3 Ibn Tofaïl University, Dept. of Mathematics, Kenitra, Morocco e-mail:


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.

Keywords: Stability; Hyperstability; Radical functional equations

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

[1] L. Aiemsomboon and W. Sintunavarat, “On generalized hyperstability of a general linear equation”, Acta mathematica hungarica, vol. 149, no. 2, pp. 413-422, Aug. 2016, doi: 10.1007/s10474-016-0621-2. [ Links ]

[2] M. Almahalebi, A. Charifi and S. Kabbaj, “Hyperstability of a Cauchy functional equation”, Journal of nonlinear analysis and optimization: theory & applications, vol. 6, no. 2, pp. 127-137, 2015. [On line]. Available: ]

[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, pp. 64-66, 1950, doi: 10.2969/jmsj/00210064. [ Links ]

[4] D. G. Bourgin, “Classes of transformations and bordering transformations”, Bulletin of the American mathematical society, vol. 57, no. 4, pp. 223-237, 1951, doi: 10.1090/S0002-9904-1951-09511-7. [ Links ]

[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 Harbor, FL: Hadronic Press, 1994, pp. 19-22. [ Links ]

[6] J. Brzdęk, J. Chudziak, and Z. Páles, “A fixed point approach to stability of functional equations”, Nonlinear analysis: theory, methods & applications, vol. 74, no. 17, pp. 6728-6732, Dec. 2011, doi: 10.1016/ [ Links ]

[7] J. Brzdęk , Hyperstability of the Cauchy equation on restricted domains, Acta mathematica hungarica , vol. 141, no. 1-2, pp. 58-67, Oct. 2013, doi: 10.1007/s10474-013-0302-3. [ Links ]

[8] J. Brzdęk , “Remark 3. 16th International Conference on Functional Equations and Inequalities, Będlewo, Poland, May 17-23, 2015”, Annales universitatis paedagogicae cracoviensis. Studia mathematica, vol. 14, no. 1, p. 196, Dec. 2015, doi: 10.1515/aupcsm-2015-0012. [ Links ]

[9] M. Eshaghi Gordji, H. Khodaei, A. Ebadian, and G. H. Kim, “Nearly radical quadratic functional equations in p-2-normed spaces”, Abstract and applied analysis, Art. ID. 896032, 2012, doi: 10.1155/2012/896032. [ Links ]

[10] D. H. Hyers, “On the stability of the linear functional equation”, Proceedings of the National Academy of Sciences of the United States of America, vol. 27, no. 4 pp. 222-224, Apr. 1941, doi: 10.1073/pnas.27.4.222. [ Links ]

[11] H. Khodaei , M. Eshaghi Gordji , S. S. Kim, and Y. J. Cho, “Approximation of radical functional equations related to quadratic and quartic mappings”, Journal of mathematical analysis and applications, vol. 395, no.1, pp. 284-297, Nov. 2012, doi: 10.1016/j.jmaa.2012.04.086. [ Links ]

[12] S. S. Kim , Y. J. Cho andM. Eshaghi Gordji , “On the generalized Hyers-Ulam-Rassias stability problem of radical functional equations”, Journal of inequalities and applications, Art. ID. 186, Aug. 2012, doi: 10.1186/1029-242X-2012-186. [ Links ]

[13] G. Maksa and Z. Pales, “Hyperstability of a class of linear functional equations”, Acta mathematica academiae paedagogicae nyiregyhaziensis, vol. 17, no. 2, pp. 107-112, 2001. [On line]. Available: Links ]

[14] Th. M. Rassias, “On the stability of the linear mapping in Banach spaces”, Proceeding of the American mathematical society, vol. 72, no. 1, pp. 297-300, 1978, doi: 10.1090/S0002-9939-1978-0507327-1. [ Links ]

[15] Th. M. Rassias, “Problem 16, 2°. The Twenty-seventh International Symposium on Functional Equations, August 14-24, 1989, Bielsko-BiałKatowice-Kraków, Poland”, Aequationes mathematicae, vol. 39, no. 2-3, pp. 292-293, Apr. 1990, doi: 10.1007/BF01833155. [ Links ]

[16] Th. M. Rassias, “On a modified Hyers-Ulam sequence”, Journal of mathematical analysis and applications , vol. 158, no. 1, pp. 106-113, Jun. 1991, doi: 10.1016/0022-247X(91)90270-A. [ Links ]

[17] S. M. Ulam, Problems in modern mathematics. New York, NY: John Wiley & Sons, 1964. [ Links ]

Received: December 2018; Accepted: June 2019

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License