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Tytuł artykułu

Stability and hyperstability of a quadratic functional equation and a characterization of inner product spaces

Wybrane pełne teksty z tego czasopisma
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Języki publikacji
EN
Abstrakty
EN
We have proved the Hyers-Ulam stability and the hyperstability of the quadratic functional equation f(x+y+z) +f(x+y−z) +f(x−y+z) +f(−x+y+z) = 4[f(x) +f(y) +f(z) ] in the class of functions from an abelian group G into a Banach space.
Wydawca
Rocznik
Strony
295--303
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
  • Department of Mathematics, Faculty of Sciences, University of Ibn Tofail, Kenitra, Morocco
autor
  • Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Republic of Korea
autor
  • Department of Mathematics, Kangnam University, Yongin, Gyoenggi 16979, Republic of Korea
Bibliografia
  • [1] Ulam S. M., Problems in Modern Mathematics, Chapter IV, Science Editions, Wiley, New York, 1960
  • [2] Hyers D. H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 1941, 27(4), 222–224
  • [3] Bourgin D. G., Approximate ly isometric and multiplicative transformations on continuous function rings, Duke Math. J., 1949,16(2), 385–397
  • [4] Aoki T., On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 1950, 2(1-2), 64–66
  • [5] Rassias T. M., On the stability of the linear mapping in Banach spaces, Proc. Am. Math. Soc., 1978, 72, 297–300
  • [6] Gajda Z., On stability of additive mappings, Int. J. Math. Math. Sci., 1991, 14(3), 431–434
  • [7] Rassias T. M., On a modified Hyers-Ulam sequence, J. Math. Anal. Appl., 1991, 158(1), 106–113
  • [8] Rassias T. M., Semrl P., On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Am. Math. Soc., 1992,114(4), 989–993
  • [9] Gӑvruta P., A generalization of the Hyers-Ulam-Rassias stability of approximate y additive mappings, J. Math. Anal, Appl.,1994, 184(3), 431–436
  • [10] Czerwik S., On the stability of the quadratic mapping in normed spaces, Bull. Abh. Math. Sem. Univ. Hamburg, 1992, 62(1),59–64
  • [11] Gordji M. E., Rahimi A., Park C., Shin D., Ternary Jordan bi-homo morphisms in Banach Lietriple systems, J. Comput. Anal. Appl., 2016, 21(6), 1040–1045
  • [12] Jung S., On the Hyers-Ulam-Rassias stability of the quadratic functional equations, J. Math. Anal. Appl., 1998, 232(2), 384–339
  • [13] Kannappan P., Quadratic functional equation and inner product spaces, Results Math., 1995, 27(3-4), 368–372
  • [14] Jung S., Quadratic functional equations of Pexider type, Int. J. Math. Math. Sci., 2000, 24(5), 351–359
  • [15] Krishnan R., Kumar M. A., On the generalized Hyers-Ulam-Rassias stability of a quadratic functional equation, Int. J. Pure Appl. Math., 2006, 28, 85–94
  • [16] Maksa G., Páles Z., Hyperstability of a class of linear functional equations, Acta Math. Acad. Paedagog. Nyházi, 2001, 17(2),107–112
  • [17] Brzdęk J., Remarks on hyperstability of the the Cauchy equation, Aequationes Math., 2013, 86, 255–267
  • [18] Brzdęk J., Hyperstability of the Cauchy equation on restricted domains, Acta Math. Hungar., 2013, 141(1-2), 58–67
  • [19] Brzdęk J., A hyperstability result for the Cauchy equation, Bull. Austral. Math. Soc., 2014, 89(1), 33–40
  • [20] Gselmann E., Hyperstability of a functional equation, Acta Math. Hungar., 2009, 124(1-2), 179–188
  • [21] Bahyrycz A., Piszczek M., Hyperstability of the Jensen functional equation, Acta Math. Hungar., 2014, 142(2), 353–365
  • [22] EL-Fassi Iz., Generalized hyerstability of a Dry gas functional equation on a restricted domain using Brzdęk’s fixed point theorem, J. Fixed Point Theory Appl., 2017, 19, 2529–2540
  • [23] Brzdęk J., Ciepliński K., Hyperstability and superstability, Abs. Appl. Anal., 2013(2013), Art. ID 401756
  • [24] Piszczek M., Remark on hyperstability of the general linear equation, Aequationes Math., 2014, 88(1-2), 163–168
  • [25] Brzdęk J., Chudziak J., Páles Z., A fixed point approach to stability of functional equations, Nonlinear Anal., 2011, 74(11),6728–6732
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-2fbf0aaf-8708-4488-89d2-63d0e39070b4
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