Some statements for bi-pseudo-integrals and the role on reconstruction of the pseudo-additive measures

  • Authors

    2015-09-18
    https://doi.org/10.14419/ijamr.v4i4.4962
  • Bi-Pseudo-Integral, Pseudo-Additive Measure, Generator, Pseudo-Operations, Reconstruction.

  • Abstract

    With the support of some very important and special generators, are given some details about the properties of bi-pseudo-integrals and above all, for the first bi-pseudo-integral the relations with integral Lebesgue are listed. Further, will be shown pseudo-linearity of bi-pseudo-integrals and some investigations in reconstructions of pseudo-additive measures by bi-pseudo-integrals synthesized the reciprocal relationship between pseudo-additive measure and bi-pseudo-integral.

    Author Biography

    • Dhurata Valera, "A. Xhuvani" University, NSF, Mathematics Department,Elbasan, ALBANIA

      Mathematics Department

      Lecturer

  • References

    1. [1] J. Acz l, “Lectures on Functional Equations and their Applicationsâ€, Academic Press, New York, (1966).

      [2] E. Pap, “g-calculusâ€, Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 23, 1(1993), pp. 145-156.

      [3] Koles rov , “A note on the â¨-measure based integralsâ€, Tatra Mauntains Math., Publ., 3 (1993), pp .173-182.

      [4] R. Mesiar, J. Ryb rik, “Pseudo-arithmetical operationsâ€, Tatra Mauntains Math., Publ., 2 (1993, pp. 185-192.

      [5] N. Ralevic Ì, “Some new properties of g-calculusâ€, Univ. Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 24, 1 (1994), pp. 139-157.

      [6] Z Rie anov , “About σ-additive measure and σ-maxitive measureâ€, Math. Slovaca, 31 (1982), pp. 389-395.

      [7] Koles rov , “Integration of real functions with respect to a â¨-measureâ€, Math.,Slovaca, 46 (1996), No. 1, pp. 41-52.

      [8] E. Pap, “Pseudo-additive measures and their applicationsâ€, in: E. Pap (Ed.), Handbook of Measure Theory, Volume II. Elsevier, Amsterdam, 2002, pp. 1405-1465. http://dx.doi.org/10.1016/B978-044450263-6/50036-1.

      [9] Dh. Valera, I. Dylgjeri, “The special role of the g–functionsâ€, Математички Билтен, ISSN 0351-336X, Vol. 38 (LXIV) No. 1, (2014), Скопје, Македонија, pp. 57-69.

      [10] Dh.Valera, “Intercourses with Bi-Pseudo-Integrals based on modified functions and measures by â€, Int. Jr. of Mathematical Sciences & Applications, Mind Reader Publications, ISSN No: 2230-9888, Vol. 5, No. 2, (2015), pp. 401-412.

      [11] Marinov , “Integrations with respect to a â¨-measureâ€, Math. Slovaca 36, (1986), pp.15-22.

      [12] N. Shilkret, “Maxitive measure and integrationâ€, Indag. Math., 33 (1971), pp. 109-116 http://dx.doi.org/10.1016/S1385-7258(71)80017-3.

      [13] Markova, “Some remark on pseudo-linear algebraâ€, Tatra Mauntains Math., Publ., 6 (1995), pp. 123-130.

      [14] J. Ryb rik,†g-FUNCTIONSâ€, Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 25, 1 (1995), pp. 29-38.

      [15] M. Sugeno,T. Murofushi, “Pseudo-additive Measure and Integralsâ€, J. Math. Appl.122 (1987), pp. 197-222. http://dx.doi.org/10.1016/0022-247x(87)90354-4.

      [16] P.Poncet, “Pseudo-multiplication and their propertiesâ€, arXiv: 1301.0761 [math.RA], 4 Jan 2013.

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  • How to Cite

    Valera, D. (2015). Some statements for bi-pseudo-integrals and the role on reconstruction of the pseudo-additive measures. International Journal of Applied Mathematical Research, 4(4), 442-453. https://doi.org/10.14419/ijamr.v4i4.4962

    Received date: 2015-06-21

    Accepted date: 2015-09-14

    Published date: 2015-09-18