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Generalized Ulam-Hyers stability of group and stability of group and ring homomorphisms via a fixed point method

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Języki publikacji
EN
Abstrakty
EN
By using the fixed point method, we investigate the generalized Hyers-Ulam stability of group homomorphisms and ring homomorphisms. Our work brings some complements and some continuations to the results obtained previously by R. Badora (On approximate ring homomorphisms published in J. Math. Anal. Appl, 276, (2002), 589-597) and those of D. Zhang and H-X. Cao (Stability of group and ring homomorphisms, Mathematical Inequalities & Applications, 9(3) (2006), 521-528).
Rocznik
Tom
Strony
23--37
Opis fizyczny
Bibliogr. 33 poz.
Twórcy
  • Department of Mathematics, Cadi Ayyad University, Faculty of Sciences, Semlalia, Av. Prince my Abdellah, B.P. 2390, Marrakech, MAROC (Morocco)
Bibliografia
  • [1] Akkouchi M., Stability of certain functional equations via a fixed point of Ćirić, Filomat, 25(2) (2011), 121-127.
  • [2] Aoki T., On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2(1950), 64-66.
  • [3] Badora R., On approximate ring homomorphisms, J. Math. Anal. Appl., 276(2002), 589-597.
  • [4] Baker J.A., The stability of certain functional equations, Proc. Amer. Math. Soc., 112(3) (1991), 729-732.
  • [5] Bourgin D.G., Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J., 16(1949), 385-397.
  • [6] Cǎdariu L., Radu V., Fixed points and the stability of quadratic functional equations, Analele Universitatii de Vest din Timisoara, 41(2003), 25-48.
  • [7] Cǎdariu L., Radu V., Fixed points and the stability of Jensen’s functional equation, J. Inequal. Pure Appl. Math., 4(2003), Art. ID 4.
  • [8] Cǎdariu L., Radu V., On the stability of the Cauchy functional equation: a fixed point approach, Grazer Mathematische Berichte, 346(2004), 43-52.
  • [9] Cǎdariu L., Radu V., The fixed points method for the stability of some functional equations, Carpathian Journal of Mathematics, 23(2007), 63-72.
  • [10] Cholewa P.W., Remarks on the stability of functional equations, Aequationes Math., 27(1984), 76-86. MR0758860 (86d:39016).
  • [11] Czerwik S., Stability of functional equations of Ulam-Hyers-Rassias type, Hadronic Press, 2003.
  • [12] Diaz J.B., Margolis B., A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74(1968), 305-309.
  • [13] Forti G.L., Hyers-Ulam stability of functional equations in several variables, Aequationes Math., 50(1995), 143-190.
  • [14] Gajda Z., On stability of additive mappings, Internat. J. Math. Math. Sci., 14(1991), 431-434.
  • [15] Gǎvruta P., A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(1994), 431-436.
  • [16] Hyers D.H., On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27(1941), 222-224.
  • [17] Hyers D.H., Isac G., RassiaTh. M. S., Stability of functional Equations in Several Variables, Birkhauser, Boston, Basel, Berlin, 1998.
  • [18] Isac G., Rassias Th.M., On the Hyers-Ulam stability of additive mappings, J. Approx. Theory, 72(1993), 131-137.
  • [19] Jung S.-M., Kim T.-S., Lee K.-S., A fixed point approach to the stability of quadratic functional equation, Bull. Korean Math. Soc., 43(3) (2006), 531-541.
  • [20] Maligranda L., A result of Tosio Aoki about a generalization of Hyers-Ulam stability of additive functions - a question of priority, Aequationes Math., 75(2008), 289-296.
  • [21] Páles Zs., Generalized stability of the Cauchy functional equation, Aequationes Math., 56(3) (1998), 222-232.
  • [22] Park C., Rassias J.M., Stability of the Jensen-type functional equation in C*-algebras: a fixed point approach, Abstract and Applied Analysis Volume 2009, Article ID 360432, 17 pages.
  • [23] Radu V., The fixed point alternative and the stability of functional equations, Fixed Point Theory, 4(2003), 91-96.
  • [24] Rassias Th.M., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72(1978) 297-300.
  • [25] Rassias Th.M., Solution of a problem of Ulam, J. Approx. Theory, 57(3) (1989), 268-273.
  • [26] Rassias Th.M., On the stability of functional equations and a problem of Ulam, Acta Math. Appl., 62(2000), 23-130.
  • [27] Rassias Th.M., On the stability of functional equations in Banach spaces, J. Math. Anal. Appl., 251(2000), 264-284.
  • [28] Rassias Th.M., The problem of S. M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl., 246(2) (2000), 352-378.
  • [29] Székelyhidi L., On a stability theorem, C. R. Math. Rep. Acad. Sci. Canada, 3(5) (1981), 253-255.
  • [30] Székelyhidi L., The stability of linear functional equations, C. R. Math. Rep. Acad. Sci. Canada, 3(2) (1981), 63-67.
  • [31] Székelyhidi L., Ulam’s problem, Hyers’s solution and to where they led, Functional Equations and Inequalities, Th. M. Rassias (Ed.) Vol. 518 of Mathematics and Its Applications, Kluwer Acad. Publ., Dordrecht, (2000), 259-285.
  • [32] Ulam S.M., Problems in Modern Mathematics, Chapter VI, science ed. Wiley, New York, 1940.
  • [33] Zhang D., Cao H.-X., Stability of group and ring homomorphisms, Mathematical Inequalities & Applications, 9(3) (2006), 521-528.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d1670fc9-61b1-490a-95de-e6b0be599872
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