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On new stability results for composite functional equations in quasi-β-normed spaces

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Języki publikacji
EN
Abstrakty
EN
In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f(f(x) – f(y)) = f(x + y) + f(x – y) – f(x) – f(y), where f maps from a(β, p)-Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite s-functional inequality is discussed via our results.
Wydawca
Rocznik
Strony
68--84
Opis fizyczny
Bibliogr. 34 poz.
Twórcy
  • Department of Mathematics, Faculty of Science and Technology, Muban Chombueng Rajabhat University, Chom Bueng, Ratchaburi, 70150, Thailand
  • Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Phatum Thani 12120, Thailand
Bibliografia
  • [1] S. M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1964.
  • [2] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. 27(1941), no. 4, 222–224.
  • [3] Th.M.Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), no. 2, 297–300.
  • [4] P. Gãvruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184(1994), 431–436.
  • [5] S. Gołąb and A. Schinzel, Sur lequation fonctionnelle f(x + f(x)y) = f(x)f(y), Publ. Math. Debrecen 6(1959), 113–125.
  • [6] J. Chudziak, On a functional inequality related to the stability problem for the Gołąb-Schinzel equation, Publ. Math. Debrecen 67(2005), no. 1-2, 199–208.
  • [7] A. Charifi, B. Bouikhalene, S. Kabbaj, and J. M. Rassias, On the stability of a pexiderized Gołąb-Schinzel equation, Comput. Math. Appl. 59(2010), 3193–3202.
  • [8] N. Brillouët-Belluot and J. Brzdęk, On continuous solutions and stability of a conditional Gołąb-Schinzel equation, Publ. Math. Debrecen 72(2008), 441–450.
  • [9] J. Chudziak, Approximate solutions of the Gołąb-Schinzel equation, J. Approx. Theory 136(2005), 21–25.
  • [10] J. Chudziak, Stability of the generalized Gołąb-Schinzel equation, Acta Math. Hungar. 113(2006), 133–144.
  • [11] J. Chudziak, Approximate solutions of the generalized Gołąb-Schinzel equation, J. Inequal. Appl. 2006(2006), 89402, DOI: https://doi.org/10.1155/JIA/2006/89402.
  • [12] J. Chudziak, Stability problem for the Gołąb-Schinzel type functional equations, J. Math. Anal. Appl. 339(2008), 454–460.
  • [13] J. Chudziak and J. Tabor, On the stability of the Gołąb-Schinzel functional equation, J. Math. Anal. Appl. 302(2005), 196–200.
  • [14] W. Fechner, On a composite functional equation on Abelian groups, Aequationes Math. 78(2009), 185–193.
  • [15] A. Tarski, Problem no. 83, Parametr 1(1930), no. 6231; Solution, Mlody Matematyk 1(1931), no. 190.
  • [16] T. Kochanek, On a composite functional equation fulfilled by modulus of an additive function, Aequationes Math. 80(2010), 155–172.
  • [17] W. Fechner, On some composite functional inequalities, Aequat. Math. 79(2010), 307–314.
  • [18] W. Fechner, Stability of a composite functional equation related to idempotent mappings, J. Approx. Theory 163(2011), 328–335.
  • [19] H. A. Kenary, Hyers-Ulam-Rassias stability of a composite functional equation in various normed spaces, Bull. Iranian Math. Soc. 39(2013), 383–403.
  • [20] S. Alshybani, S. M. Vaezpour, and R. Saadati, Stability of the sextic functional equation in various spaces, J. Inequal. Spec. Funct. 9(2018), no. 4, 8–27.
  • [21] Y. Ding, T. Z. Xu, and J. M. Rassias, On Ulam-Hyers stability of decic functional equation in non-Archimedean spaces, J. Comput. Anal. Appl. 26(2019), no. 4, 671–677.
  • [22] A. Magesh, R. Veera Sivaji, and A. Ponmana Selvan, Stability of quintic functional equation in matrix normed apaces: A fixed point approach, Int. J. Sci. Eng. Sci. 1(2017), no. 7, 65–69.
  • [23] M. Nazarianpoor, J. M. Rassias, and Gh. Sadeghi, Stability and nonstability of octadecic functional equation in multi-normed spaces, Arab. J. Math. 7(2018), 219–228, DOI: https://doi.org/10.1007/s40065-017-0186-0.
  • [24] J. M. Rassias, K. Ravi, and B. V. Senthil Kumar, A fixed point approach to Ulam-Hyers stability of duodecic functional equation in quasi-β-normed spaces, Tbilisi Math. J.10(2017), no. 4, 83–101.
  • [25] J. M. Rassias, S. S. Kim, and S. H. Kim, Solution and stability of nonic functional equations in non-Archimedean normed spaces, J. Comput. Anal. Appl. 24(2018), no. 6, 1162–1174.
  • [26] K. Ravi, J. M. Rassias, and B. V. Senthil Kumar, Ulam-Hyers stability of undecic functional equation in quasi-β-normed spaces: Fixed point method, Tbilisi J. Math. 9(2016), no. 2, 83–103, DOI: https://doi.org/10.1515/tmj-2016-0022.
  • [27] Y. Shen and W. Chen, On the stability of septic and octic functional equations, J. Comput. Anal. Appl. 18(2015), no. 2, 277–290.
  • [28] S. Rolewicz, Metric Linear Spaces, PWN-Polish Sci. Publ., Warszawa, Reidel, Dordrecht, 1984.
  • [29] S. Czerwik,Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Math. Fis. Univ. Modena 46 (1998), 263–276.
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  • [31] H. Aydi and S. Czerwik, Fixed point theorems in generalizes b-metric spaces, in: N. Daras, T. Rassias (eds.), Modern Discrete Mathematics and Analysis, Springer Optimization and Its Applications, vol. 131, Springer, Cham, 2018, pp. 1–9, DOI: https://doi.org/10.1007/978-3-319-74325-7_1.
  • [32] C. Park, J. R. Lee, and X. H. Zhang, Additive s-functional inequality and hom-derivations in Banach algebras, J. Fixed Point Theory Appl. 21(2019), 18, DOI: https://doi.org/10.1007/s11784-018-0652-0.
  • [33] N. V. Dung and V. T. L. Hang, The generalized hyperstability of general linear equations in quasi-Banach spaces, J. Math. Anal. Appl. 462(2018), 131–147, DOI: https://doi.org/10.1016/j.jmaa.2018.01.070.
  • [34] Iz-I. EL-Fassi, On the general solution and hyperstability of the general radical quintic functional equation in quasi-β-Banach spaces, J. Math. Anal. Appl. 466(2018), 733–748, DOI: https://doi.org/10.1016/j.jmaa.2018.06.024.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-12ab7bf3-8d1b-44cf-9263-834f6c4146ac
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