Hyperstability of cubic functional equation in ultrametric spaces
Resumen
In this paper, we present the hyperstability results of cubic functional equations in ultrametric Banach spaces.Citas
[1] M. Almahalebi, A. Charifi and S. Kabbaj, Hyperstability of a monomial functional equation, Journal of Scientific Research Reports, 3 (20), pp. 2685-2693, (2014).
[2] M. Almahalebi and S. Kabbaj, Hyperstability of Cauchy-Jensen type functional equation, Advances in Research, 2 (12), pp. 1017-1025, (2014).
[3] M. Almahalebi and C. Park, On the hyperstablity of a functional equa- tion in commutative groups, Journal of Computational Analysis and Applications, 20 (5) (2016), pp. 826-833, (2016).
[4] M. Almahalebi, A. Charifi and S. Kabbaj, Hyperstability of a Cauchy functional equation, Journal of Nonlinear Analysis and Optimization: Theory & Applications, (In press).
[5] M. Almahalebi, On the hyperstability of σ-Drygas functional equation on semigroups, Aequationes math., 90 4, pp. 849-857, (2016).
[6] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2, pp. 64-66, (1950).
[7] A. Bahyrycz, J. Brzd¸ek and M. Piszczek, On approximately p-Wright afine functions in ultrametric spaces, J. Funct. Spaces Appl., Art. ID 723545, (2013).
[8] A. Bahyrycz and M. Piszczek, Hyperstability of the Jensen functional equation,ActaMath.Hungar.,142, pp. 353-365, (2014).
[9] A. Bahyrycz and J. Olko, Stability of the equation of (p,q)-Wright functions,ActaMath.Hung.,146, pp. 71-85, (2015).
[10] A. Bahyrycz and J. Olko, On stability of the general linear equation, Aequationes Math., 89, pp. 1461-1474, (2015).
[11] D. G. Bourgin, Approximately isometric and multiplicative transfor- mations on continuous function rings, Duke Math. J. 16, pp. 385-397, (1949).
[12] J. Brzd¸ek, J. Chudziak and Zs. P´ales, A fixed point approach to stability of functional equations, Nonlinear Anal., 74, pp. 6728-6732, (2011).
[13] J. Brzd¸ek and K. Cieplinski, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces, Nonlinear Analysis 74, pp. 6861-6867, (2011).
[14] J. Brzd¸ek, Stability of additivity and fixed point methods, Fixed Point Theory and App., pp. 2013:285, 9 pages, (2013).
[15] J. Brzd¸ek, Hyperstability of the Cauchy equation on restricted domains, Acta Math. Hungar., 141, pp. 58-67, (2013).
[16] J. Brzd¸ek, Remarks on hyperstability of the Cauchy functional equa- tion, Aequationes Math., 86, pp. 255-267, (2013).
[17] J. Brzd¸ek, A hyperstability result for the Cauchy equation,Bull.Aust. Math. Soc., 89, pp. 33-40, (2014).
[18] J. Brzd¸ek and K. Cieplinski, Hyperstability and superstability,Abs. Appl. Anal., 2013, Article ID 401756, 13, (2013).
[19] J. Erdos, A remark on the paper On some functional equations by S. Kurepa, Glasnik Mat.-Fiz. Astronom., 14, pp. 3-5, (1959).
[20] P. Gavrut¸a, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184, pp. 431- 436, (1994).
[21] E. Gselmann, Hyperstability of a functional equation, Acta Math. Hun- gar., 124, pp. 179-188, (2009).
[22] D. H. Hyers, On the stability of the linear functional equation,Proc. Natl. Acad. Sci. U.S.A., 27, pp. 222-224, (1941).
[23] B. Jessen, J. Karpf and A. Thorup, Some functional equations in groups and rings, Math. Scand., 22, pp. 257-265, (1968).
[24] A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dy- namical Systemsand Biological Models. , Kluwer Academic Publishers, Dordrecht, (1997).
[25] Gy. Maksa and Zs. Páles, Hyperstability of a class of linear functional equations, Acta Math., 17 (2), pp. 107-112, (2001).
[26] M. Piszczek, Remark on hyperstability of the general linear equation, Aequationes math., 88 (1), pp. 163-168, (2014).
[27] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, pp. 297-300, (1978).
[28] M. Sirouni and S. Kabbaj, A fixed point approach to the hyperstability of Drygas functional equation in metric spaces.J.Math.Comput.Sci., 4 (4), pp. 705-715, (2014).
[29] S. M. Ulam, Problems in Modern Mathematics, Science Editions, John- Wiley & Sons Inc. New York, (1964).
[30] D. Zhang, On Hyers-Ulam stability of generalized linear functional equation and its induced Hyers-Ulam programming problem,Aequa- tiones Math., 90, pp. 559-568, (2016).
[31] D. Zhang, On hyperstability of generalised linear functional equations in several variables, Bull. Aust. Math. Soc., 92, pp. 259-267, (2015).
[2] M. Almahalebi and S. Kabbaj, Hyperstability of Cauchy-Jensen type functional equation, Advances in Research, 2 (12), pp. 1017-1025, (2014).
[3] M. Almahalebi and C. Park, On the hyperstablity of a functional equa- tion in commutative groups, Journal of Computational Analysis and Applications, 20 (5) (2016), pp. 826-833, (2016).
[4] M. Almahalebi, A. Charifi and S. Kabbaj, Hyperstability of a Cauchy functional equation, Journal of Nonlinear Analysis and Optimization: Theory & Applications, (In press).
[5] M. Almahalebi, On the hyperstability of σ-Drygas functional equation on semigroups, Aequationes math., 90 4, pp. 849-857, (2016).
[6] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2, pp. 64-66, (1950).
[7] A. Bahyrycz, J. Brzd¸ek and M. Piszczek, On approximately p-Wright afine functions in ultrametric spaces, J. Funct. Spaces Appl., Art. ID 723545, (2013).
[8] A. Bahyrycz and M. Piszczek, Hyperstability of the Jensen functional equation,ActaMath.Hungar.,142, pp. 353-365, (2014).
[9] A. Bahyrycz and J. Olko, Stability of the equation of (p,q)-Wright functions,ActaMath.Hung.,146, pp. 71-85, (2015).
[10] A. Bahyrycz and J. Olko, On stability of the general linear equation, Aequationes Math., 89, pp. 1461-1474, (2015).
[11] D. G. Bourgin, Approximately isometric and multiplicative transfor- mations on continuous function rings, Duke Math. J. 16, pp. 385-397, (1949).
[12] J. Brzd¸ek, J. Chudziak and Zs. P´ales, A fixed point approach to stability of functional equations, Nonlinear Anal., 74, pp. 6728-6732, (2011).
[13] J. Brzd¸ek and K. Cieplinski, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces, Nonlinear Analysis 74, pp. 6861-6867, (2011).
[14] J. Brzd¸ek, Stability of additivity and fixed point methods, Fixed Point Theory and App., pp. 2013:285, 9 pages, (2013).
[15] J. Brzd¸ek, Hyperstability of the Cauchy equation on restricted domains, Acta Math. Hungar., 141, pp. 58-67, (2013).
[16] J. Brzd¸ek, Remarks on hyperstability of the Cauchy functional equa- tion, Aequationes Math., 86, pp. 255-267, (2013).
[17] J. Brzd¸ek, A hyperstability result for the Cauchy equation,Bull.Aust. Math. Soc., 89, pp. 33-40, (2014).
[18] J. Brzd¸ek and K. Cieplinski, Hyperstability and superstability,Abs. Appl. Anal., 2013, Article ID 401756, 13, (2013).
[19] J. Erdos, A remark on the paper On some functional equations by S. Kurepa, Glasnik Mat.-Fiz. Astronom., 14, pp. 3-5, (1959).
[20] P. Gavrut¸a, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184, pp. 431- 436, (1994).
[21] E. Gselmann, Hyperstability of a functional equation, Acta Math. Hun- gar., 124, pp. 179-188, (2009).
[22] D. H. Hyers, On the stability of the linear functional equation,Proc. Natl. Acad. Sci. U.S.A., 27, pp. 222-224, (1941).
[23] B. Jessen, J. Karpf and A. Thorup, Some functional equations in groups and rings, Math. Scand., 22, pp. 257-265, (1968).
[24] A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dy- namical Systemsand Biological Models. , Kluwer Academic Publishers, Dordrecht, (1997).
[25] Gy. Maksa and Zs. Páles, Hyperstability of a class of linear functional equations, Acta Math., 17 (2), pp. 107-112, (2001).
[26] M. Piszczek, Remark on hyperstability of the general linear equation, Aequationes math., 88 (1), pp. 163-168, (2014).
[27] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, pp. 297-300, (1978).
[28] M. Sirouni and S. Kabbaj, A fixed point approach to the hyperstability of Drygas functional equation in metric spaces.J.Math.Comput.Sci., 4 (4), pp. 705-715, (2014).
[29] S. M. Ulam, Problems in Modern Mathematics, Science Editions, John- Wiley & Sons Inc. New York, (1964).
[30] D. Zhang, On Hyers-Ulam stability of generalized linear functional equation and its induced Hyers-Ulam programming problem,Aequa- tiones Math., 90, pp. 559-568, (2016).
[31] D. Zhang, On hyperstability of generalised linear functional equations in several variables, Bull. Aust. Math. Soc., 92, pp. 259-267, (2015).
Publicado
2017-10-20
Cómo citar
Aribou, Y., Almahalebi, M., & Kabbaj, S. (2017). Hyperstability of cubic functional equation in ultrametric spaces. Proyecciones. Journal of Mathematics, 36(3), 461-484. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2391
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