Abstract
In this paper, we present hyperstability results of Jensen functional equations in ultrametric Banach spaces.
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Almahalebi, M., Charifi, A., Kabbaj, S.: Hyperstability of a monomial functional equation. J. Sci. Res. Rep. 3(20), 2685–2693 (2014)
Almahalebi, M., Kabbaj, S.: Hyperstability of Cauchy–Jensen type functional equation. Adv. Res. 2(12), 1017–1025 (2014)
Almahalebi, M., Park, C.: On the hyperstablity of a functional equation in commutative groups. J. Comput. Anal. Appl. 20(5), 826–833 (2016)
Almahalebi, M., Charifi, A., Kabbaj, S.: Hyperstability of a Cauchy functional equation. J. Nonlinear Anal. Optim. 6(2), 127–137 (2015)
Almahalebi, M.: On the hyperstability of \(\sigma \)-Drygas functional equation on semigroups. Aequat. Math. 90(4), 849–857 (2016)
Bahyrycz, A., Brzdȩk, J., Piszczek, M.: On approximately \(p\)-Wright affine functions in ultrametric spaces. J. Funct. Spaces Appl., Art. ID 723545 (2013)
Bahyrycz, A., Piszczek, M.: Hyperstability of the Jensen functional equation. Acta Math. Hung. 142, 353–365 (2014)
Bahyrycz, A., Olko, J.: Stability of the equation of \((p, q)\)-Wright functions. Acta Math. Hung. 146, 71–85 (2015)
Bahyrycz, A., Olko, J.: On stability of the general linear equation. Aequat. Math. 89, 1461–1474 (2015)
Bourgin, D.G.: Approximately isometric and multiplicative transformations on continuous function rings. Duke Math. J. 16, 385–397 (1949)
Brzdȩk, J., Chudziak, J., Páles, Zs: A fixed point approach to stability of functional equations. Nonlinear Anal. 74, 6728–6732 (2011)
Brzdȩk, J., Ciepliñski, K.: A fixed point approach to the stability of functional equations in non-Archimedean metric spaces. Nonlinear Anal. 74, 6861–6867 (2011)
Brzdȩk, J.: Stability of additivity and fixed point methods. Fixed Point Theory Appl. 2013, 285 (2013)
Brzdȩk, J.: Hyperstability of the Cauchy equation on restricted domains. Acta Math. Hung. 141, 58–67 (2013)
Brzdȩk, J.: Remarks on hyperstability of the Cauchy functional equation. Aequat. Math. 86, 255–267 (2013)
Brzdȩk, J.: A hyperstability result for the Cauchy equation. Bull. Aust. Math. Soc. 89, 33–40 (2014)
Brzdȩk, J., Ciepliñski, K.: Hyperstability and superstability. Abstr. Appl. Anal. 2013, Article ID 401756 (2013)
Găvruţa, P.: A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184, 431–436 (1994)
Gselmann, E.: Hyperstability of a functional equation. Acta Math. Hung. 124, 179–188 (2009)
Hyers, D.H.: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222–224 (1941)
Khrennikov, A.: Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models. Kluwer Academic Publishers, Dordrecht (1997)
Maksa, G., Páles, Z.: Hyperstability of a class of linear functional equations. Acta Math. 17(2), 107–112 (2001)
Moszner, Z.: Stability has many names. Aequat. Math. 90, 983–999 (2016)
Piszczek, M.: Remark on hyperstability of the general linear equation. Aequat. Math. 88(1), 163–168 (2014)
Rassias, ThM: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978)
Sirouni, M., Kabbaj, S.: A fixed point approach to the hyperstability of Drygas functional equation in metric spaces. J. Math. Comput. Sci. 4(4), 705–715 (2014)
Ulam, S.M.: Problems in Modern Mathematics, Science Editions. Wiley, New York (1964)
Zhang, D.: On Hyers–Ulam stability of generalized linear functional equation and its induced Hyers–Ulam programming problem. Aequat. Math. 90, 559–568 (2016)
Zhang, D.: On hyperstability of generalised linear functional equations in several variables. Bull. Aust. Math. Soc. 92, 259–267 (2015)
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Almahalebi, M., Chahbi, A. Hyperstability of the Jensen functional equation in ultrametric spaces. Aequat. Math. 91, 647–661 (2017). https://doi.org/10.1007/s00010-017-0487-6
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DOI: https://doi.org/10.1007/s00010-017-0487-6