Hyers-Ulam stability of an additive-quadratic functional equation

• Autores: Vediyappan Govindan, Choonkil Park, Sandra Pinelas, Themistocles M. Rassias
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 22, Nº. 2, 2020, págs. 233-255
• Idioma: inglés
• DOI: 10.4067/S0719-06462020000200233
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen En este artículo introducimos la siguiente ecuación funcional de tipo (a, b, c)-mixta de la forma donde a, b, c son enteros positivos con a > 1, e investigamos la solución y la estabilidad de Hyers-Ulam de la ecuación funcional anterior en espacios de Banach usando dos métodos diferentes.

  • English

    Abstract In this paper, we introduce the following (a, b, c)-mixed type functional equation of the form where a, b, c are positive integers with a > 1, and investigate the solution and the Hyers-Ulam stability of the above functional equation in Banach spaces by using two different methods.

• Referencias bibliográficas
  • Aczel, J.,Dhombres, J.. (1989). Functional equations in several variables. Cambridge University Press. Cambridge.
  • Aiemsomboon, L.,Sintunavarat, W.. (2018). Stability of the generalized logarithmic functional equations arising from fixed point theory. Rev....
  • Aoki, T.. (1950). On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan. 2. 64
  • Chang, I.,Lee, E.,Kim, H.. (2003). On the Hyers-Ulam-Rassias stability of a quadratic functional equations. Math. Inequal. Appl.. 6. 87-95
  • Cieplinski, K.. (2012). Applications of fixed point theorems to the Hyers-Ulam stabiltiy of functional equations - a survey. Ann. Funct. Anal.....
  • Czerwik, St.. (1992). On the stability of the quadratic mapping in normed spaces. Abh. Math. Sem. Univ. Hamburg. 62. 59-64
  • Czerwik, S.. (2002). Functional equations and inequalities in several variables,. World Scientific Publishing Co., Inc.. River Edge, NJ,.
  • Ebadian, A.,Ghobadipour, N.,Eshaghi Gordji, M.. (2010). A fixed point method for perturbation of bimultipliers and Jordan bimultipliers in...
  • Govindan, V.,Murthy, S.,Saravanan, M.. (2020). Solution and stability of a cubic type functional equation: Using direct and fixed point methods....
  • Gavruta, P.. (1994). A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings. J. Math. Anal. Appl.. 184. 431
  • Hadzic, O.,Pap, E.. (2001). Fixed point theory in probabilistic metric spaces. Kluwer Academic Publishers. Dordrecht.
  • Hyers, D. H.,Isac, G.,Rassias, T. M.. (1998). Stability of functional equations in several variables. Birkhauser Boston, Inc.. Boston, MA,.
  • Jun, K.,Kim, H.. (2005). On the Hyers-Ulam-Rassias stability of a generalized quadratic and additive type functional equation. Bull. Korean...
  • Jung, S.-M.. (2001). Hyers-Ulam-Rassias stability of functional equations in mathematical analysis. Hadronic Press, Inc.. Palm Harbor, FL,.
  • Jung, Y.. (2008). The Ulam-Gavruta-Rassias stability of module left derivations. J. Math. Anal. Appl.. 339. 108
  • Kannappan, Pl.. (1995). Quadratic functional equation and inner product spaces. Results Math.. 27. 368
  • Lee, Y.,Jung, S.-M.,Rassias, M. T.. (2018). Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation.....
  • Lee, Y.. (2019). Generalized Hyers-Ulam stability of the pexider functional equation. Math.. 7.
  • Mirzavaziri, M.,Moslehian, M. S.. (2006). A fixed point approach to stability of a quadratic equation. Bull. Braz. Math. Soc.. 37. 361
  • Moslehian, M. S.,Rassias, Th. M.. (2007). Stabiltiy of functional equations in non-Archimedean spaces. Appl. Anal. Discrete Math.. 325
  • Najati, A.,Moghini, M. B.. (2008). On the stabiltiy of a quadratic and additive functional equation. J. Math. Anal. Appl.. 337. 399-415
  • Park, C.. (2019). Additive s-functional inequalities and partial multipliers in Banach algebras. J. Math. Inequal.. 13. 867
  • Park, C.,Lee, J. R.,Zhang, X.. (2019). Additive s-functional inequality and hom-derivations in Banach algebras. J. Fixed Point Theory Appl.....
  • Park, C.,Rassias, T. M.. (2009). Fixed points and stability of the Cauchy functional equation. Aust. J. Math. Anal. Appl.. 6. 9
  • Skof, F.. (1983). Proprieta locali e approssimazione di operatori. Rend. Semin. Mat. Fis. Milano. 53. 113
  • Rassias, T. M.. (1978). On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc.. 72. 297-300
  • Sirovnik, N.. (2014). On certain functional equation in semiprime rings and standard operator algebras. Cubo. 16. 73-80
  • Ulam, S. M.. (1964). Problems in modern mathematics. John Wiley & Sons, Inc.,. New York.