Generalized hyperstability of the cubic functional equation in ultrametric spaces

Subject Areas : Fixed point theory

Y.  ‎Aribou ¹ (Department of Mathematics, Faculty of Sciences, University of Ibn Tofail, BP 133 Kenitra, Morocco)
H.  Dimou ² (Department of Mathematics, Faculty of Sciences, University of Ibn Tofail, BP 133 Kenitra, Morocco)
S.  Kabbaj ³ (Department of Mathematics, Faculty of Sciences, University of Ibn Tofail, BP 133 Kenitra, Morocco)

Received: 2018-04-25 Accepted : 2019-02-20 Published : 2019-06-01

Keywords:

References:

[1] M. Almahalebi, On the hyperstability of σ-Drygas functional equation on semigroups, Aequationes math. 90 (4) (2016), 849-857.

[2] M. Alamahalebi, A. Chahbi, Hyperstability of the Jensen functional equation in ultrametric  spaces, In press.

[3] A. Bahyrycz, J. Brzd¸ek, M. Piszczek, On approximately p-wright afine functions in ultrametric spaces, J. Funct. Spaces Appl. (2013), 2013:723545.

[4] A. Bahyrycz, M. Piszczek, Hyperstability of the Jensen functional equation, Acta Math. Hungar. 142 (2014), 353-365.

[5] D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385-397.

[6] J. Brzdek, A hyperstability result for the Cauchy equation, Bull. Aust. Math. Soc. 89 (2014), 33-40.

[7] J. Brzdek, Hyperstability of the Cauchy equation on restricted domains, Acta Math. Hungar. 141 (1-2) (2013), 58-67.

[8] J. Brzdek, Remarks on hyperstability of the Cauchy functional equation, Aequationes Math. 86 (2013), 255-267.

[9] J. Brzdek, Stability of additivity and fixed point methods, Fixed Point Theory Appl. (2013), 2013:285.

[10] J. Brzdek, J. Chudziak, Zs. Pales, A fixed point approach to stability of functional equations, Nonlinear Anal. 74 (2011), 6728-6732.

[11] J. Brzdek, K. Cieplinski, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces, Nonlinear Analysis 74 (2011), 6861-6867.

[12] J. Brzdek, K. Cieplinski, Hyperstability and superstability, Abs. Appl. Anal. (2013), 2013:401756.

[13] P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436.

[14] E. Gselmann, Hyperstability of a functional equation, Acta. Math. Hungar. 124 (2009), 179-188.

[15] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224.

[16] A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer Academic Publishers, Dordrecht, 1997.

[17] Gy. Maksa, Zs. P´ales, Hyperstability of a class of linear functional equations, Acta. Math. 17 (2) (2001), 107-112.

[18] M. Piszczek, Remark on hyperstability of the general linear equation, Aequationes. Math. 88 (1) (2014), 163-168.

[19] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

[20] S. M. Ulam, Problems in Modern Mathematics, Science Editions, John-Wiley & Sons Inc, New York, 1964.