Generalized Hyers-Ulam-Rassisa Stability of An Additive (β1,β2)-Functional Inequalities With n- Variables In Complex Banach Space

  • Authors

    • ly van an
    2022-10-04
    https://doi.org/10.14419/gjma.v10i1.32143
  • Additive (β1, β2)-functional inequality, fixed point method, direct method, Banach space, Hyers−Ulam stability.

  • Abstract

    In this paper we study to solve the o f additive (β1,β2)-f unctional inequality with n−variables and their Hyers-Ulam stability. First are investigated in complex Banach spaces with a fixed point method and last are investigated in complex Banach spaces with a direct method. I will show that the solutions of the additive (β1,β2)-f unctional inequality are additive mapping. Then Hyers−Ulam stability o f these equation are given and proven. T hese are the main results o f this paper .


  • References

    1. [1] T.Aoki, On the stability of the linear transformation in Banach space, J. Math. Soc. Japan 2(1950), 64-66.

      [2] A.Bahyrycz, M. Piszczek, Hyers stability of the Jensen function equation, Acta Math. Hungar.,142 (2014),353-365.

      [3] Ly Van An, Hyers-Ulam stability of functional inequalities with three variable in Banach spaces and Non-Archemdean Banach spaces International

      Journal of Mathematical Analysis Vol.13, 2019, no. 11. 519-53014), 296-310..https://doi.org/10.12988/ijma.2019.9954.

      [4] Ly Van An, Hyers-Ulam stability of β-functional inequalities with three variable in non-Archemdean Banach spaces and complex Banach spaces Inter-

      national Journal of Mathematical Analysis Vol. 14, 2020, no. 5, 219 - 239 .HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2020.91169.

      https://doi.org/10.12988/ijma.2019.9954.

      [5] M.Balcerowski, On the functional equations related to a problem of z Boros and Z. Dr Ìoczy, Acta Math. Hungar.,138 (2013), 329-340.

      [6] L. CADARIU ? , V. RADU, Fixed points and the stability of Jensen’s functional equation, J. Inequal. Pure Appl. Math. 4, no. 1, Art. ID 4 (2003).

      [7] J. DIAZ, B. MARGOLIS, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Am. Math. Soc. 74

      (1968), 305-309.

      [8] W Fechner, On some functional inequalities related to the logarithmic mean, Acta Math., Hungar., 128 (2010,)31-45, 303-309 .

      [9] W. Fechner, Stability of a functional inequlities associated with the Jordan-von Neumann functional equation, Aequationes Math. 71 (2006), 149-161.

      [10] Pascus. Ga ̆vruta, A generalization of the Hyers-Ulam -Rassias stability of approximately additive mappings, Journal of mathematical Analysis and

      Aequations 184 (3) (1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211.

      [11] Attila Gil Ìanyi, On a problem by K. Nikodem, Math. Inequal. Appl., 5 (2002), 707-710.

      [12] Attila Gil Ìanyi, Eine zur parallelogrammleichung ̈aquivalente ungleichung, Aequations 5 (2002),707-710. https: //doi.org/ 10.7153/mia-05-71.

      [13] Donald H. Hyers, On the stability of the functional equation, Proceedings of the National Academy of the United States of America, 27 (4) (1941),

      222.https://doi.org/10.1073/pnas.27.4.222

      [14] Jung Rye Lee, Choonkil Park, and Dong Yun Shin. Additive and quadratic functional in equalities in Non-Archimedean normed spaces, International

      Journal of Mathematical Analysis, 8 (2014), 1233-1247. https://doi.org/10.12988/ijma.2019.9954.

      [15] L.Maligranda.Tosio Aoki (1910-1989). International symposium on Banach and function spaces:14/09/2006-17/09/2006, pages 1–23. Yokohama

      Publishers, 2008.

      [16] D. MIHET ̧, V. RADU, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008), 567-572.

      [17] A.Najati and G. Z. Eskandani.Stability of a mixed additive and cubic functional equation in quasi-Banach spaces. J. Math. Anal. Appl., 342(2):1318–1331,

      2008.

      [18] C.Park, Y. Cho, M.Han. Functional inequalities associated with Jordan-von Newman-type additive functional equations , J. Inequality .Appl. ,2007(2007),

      Article ID 41820, 13 pages.

      [19] W. P and J. Schwaiger, A system of two in homogeneous linear functional equations, Acta Math. Hungar 140 (2013), 377-406 .

      [20] Jurg ̈ Ra ̈tz On inequalities assosciated with the jordan-von neumann functional equation, Aequationes matheaticae, 66 (1) (2003), 191-200 https;//

      doi.org/10-1007/s00010-0032684-8.

      [21] Choonkil. Park. The stability an of additive (β1,β2

      -functional inequality in Banach space

      Journal of mathematical Inequalities Volume 13, Number 1 (2019), 95-104.

      [22] Choonkil. Park. Additive β-functional inequalities, Journal of Nonlinear Science and Appl. 7(2014), 296-310.

      [23] Choonkil Park, functional in equalities in Non-Archimedean normed spaces. Acta Mathematica Sinica, English Series, 31 (3), (2015), 353-366.

      https://doi.org/10.1007/s10114-015-4278-5.

      [24] C. PARK, Additive Ï-functional inequalities and equations, J. Math. Inequal. 9 (2015), 17-26.

      [25] C. PARK, Additive Ï-functional inequalities in non-Archimedean normed spaces, J. Math. Inequal. 9 (2015), 397-407.

      [26] Themistocles M. Rassias, On the stability of the linear mapping in Banach space, proceedings of the American Mathematical Society, 27 (1978),

      297-300. https: //doi.org/10.2307 /s00010-003-2684-8.

      [27] F. SKOF, Propriet locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano 53 (1983),113-129.

      [28] S. M. ULam. A collection of Mathematical problems, volume 8, Interscience Publishers. New York,1960.


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  • How to Cite

    an, ly van. (2022). Generalized Hyers-Ulam-Rassisa Stability of An Additive (β1,β2)-Functional Inequalities With n- Variables In Complex Banach Space. Global Journal of Mathematical Analysis, 10(1), 7-20. https://doi.org/10.14419/gjma.v10i1.32143

    Received date: 2022-08-03

    Accepted date: 2022-08-27

    Published date: 2022-10-04