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The new investigation of the stability ofmixed type additive-quartic functionalequations in non-Archimedean spaces

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Języki publikacji
EN
Abstrakty
EN
In this article, we prove the generalized Hyers-Ulam stability for the following additive-quarticfunctional equation: f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) + 24f(y) = 13[ f(x + y) + f(x - y)] + 12f(2y), where f maps from an additive group to a complete non-Archimedean normed space.
Wydawca
Rocznik
Strony
174--192
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
  • Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Phatum Thani 12120, 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. Natl. Acad. Sci. U.S.A. 27(1941), no. 4, 222-224, DOI: 10.1073/pnas.27.4.222.
  • [3] Tosio Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Jpn. 2(1905), no. 1-2, 64-66, DOI: 10.2969/jmsj/00210064.
  • [4] Themistocles M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Am. Math. Soc. 72(1978), no. 2, 297-300, DOI: 10.2307/2042795.
  • [5] John Michael Rassias, Solution of the Ulam stability problem for quartic mappings, Glas. Mat. Ser. 34(1999), no. 2, 243-252.
  • [6] Jukang K. Chung and Prasanna K. Sahoo, On the general solution of a quartic functional equation, Bull. Korean Math. Soc. 40(2003), no. 4, 565-576, DOI: 10.4134/BKMS.2003.40.4.565.
  • [7] Prasanna K. Sahoo, On a functional equation characterizing polynomials of degree three, Bull. Inst. Math. Acad. Sin. 32(2004), no. 1, 35-44.
  • [8] Montakarn Petapirak and Paisan Nakmahachalasint, A quartic functional equation and its generalized Hyers-Ulam-Rassias stability, Thai J. Math. 6(2008), no. 3, 77-84.
  • [9] M. Eshaghi Gordji, Stability of a functional equation deriving from quartic and additive functions, Bull. Korean Math. Soc. 47(2010), no. 3, 491-502, DOI: 10.4134/BKMS.2010.47.3.491.
  • [10] Charinthip Hengkrawit and Anurak Thanyacharoen,A general solution of a generalized quartic functional equation and its stability, Int. J. Pure Appl. Math. 80(2013), no. 4, 691-706, DOI: 10.12732/ijpam.v85i4.6.
  • [11] Jeongwook Chang, Chang-Kwon Choi, Jooyoung Kim, and Prasanna K. Sahoo, Stability of the cosine-sine functional equation with involution, Adv. Oper. Theory 2(2017), no. 4, 531-546, DOI: 10.22034/aot.1706-1190.
  • [12] Chang-Kwon Choi, Jaeyoung Chung, Riedel Thomas, and Prasanna K. Sahoo, Stability of functional equations arising from number theory and determinant of matrices, Ann. Funct. Anal. 8(2017), no. 3, 329-340, DOI: 10.1215/20088752-0000017X.
  • [13] Charinthip Hengkrawit and Anurak Thanyacharoen, A generalized additive-quartic functional equation and its stability, Bull. Korean Math. Soc.52(2015), no. 6, 1759-1776, DOI: 10.4134/BKMS.2015.52.6.1759.
  • [14] Von K. Hensel, Uber eine neue Begrundung der Theorie der algebraischen Zahlen, Jahres-ber. Deutsch. Math. 6(1897), 83-88.
  • [15] L. M. Arriola and W. A. Beyer, Stability of the Cauchy functional equation over p-adic fields, Real Anal. Exchange 31(2005/2006), no. 1, 125-132.
  • [16] Z. Kaiser, On stability of the Cauchy equation in normed spaces over fields with valuation, Publ. Math. Debrecen 64(2004), no. 1-2, 189-200.
  • [17] Mohammad Sal Moslehian and Themistocles M. Rassias, Stability of functional equations in non-Archimedean spaces, Appl. Anal. Discrete Math. 1(2007), no. 2, 325-334, DOI: 10.2298/AADM0702325M.
  • [18] J. B. Diaz and Beatriz Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Am. Math. Soc. 74(1968), no. 2, 305-309.
  • [19] Krzysztof Cieplinski, Applications of fixed point theorems to the Hyers-Ulam stability of functional equations - a survey, Ann. Funct. Anal. 3(2012), no. 1, 151-164, DOI: 10.15352/afa/1399900032.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
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Bibliografia
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bwmeta1.element.baztech-a26d76e3-e805-4f27-bf9f-59a4f18ebd98
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