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ON LINE AND DOUBLE MULTIPLICATIVE INTEGRALS

Yıl 2013, Cilt: 3 Sayı: 1, 103 - 107, 01.06.2013

Öz

In the present paper the concepts of line and double integrals are modified to the multiplicative case. Two versions of the fundamental theorem of calculus for line and double integrals are proved in the multiplicative case.

Kaynakça

  • [1] Aniszewska, D., (2007), Multiplicative Runge-Kutta method, Nonlinear Dynamics, 50, 265-272.
  • [2] Bashirov, A. E. and Bashirova, G., (2011), Dynamics of literary texts, Online Journal of Communication and Media Techniligies, 1 (3), 60-82.
  • [3] Bashirov, A. E., Kurpınar, E. and Ozyapıcı, A., (2008), Multiplicative calculus and its applications, ¨ Journal of Mathematical Analysis and Applications, 337 (1), 36-48.
  • [4] Bashirov, A. E., Kurpınar, E., Tandoˇgdu, Y. and Ozyapıcı, A., (2011), On modeling with multiplica- ¨ tive differential equations, Applied Mathematics - A Journal of Chinees Universities, 26(4), 425-438.
  • [5] Bashirov, A. E. and Riza, M., (2011), On complex multiplicative differentiation, TWMS Journal of Applied Engineering Mathematics, 1(1), 75-85.
  • [6] C´ordova-Lepe, F., (2006), The multiplicative derivative as a measure of elasticity in economics, TEMAT-Theaeteto Atheniensi Mathematica, 2(3), online.
  • [7] Daletskii, Yu. L. and Teterina, N. I., (1972), Multiplicative stochastic integrals, Uspekhi Matematicheskikh Nauk, 27(2:164), 167-168.
  • [8] Grossman, M. and Katz, R., (1972), Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA.
  • [9] Grossman, M., (1983), Bigeometric Calculus: A System with a Scale-Free Derivative, Archimedes Foundation, Rockport, MA.
  • [10] Karandikar, R. L., (1982), Multiplicative decomposition of non-singular matrix valued continuous semimartingales, The Annals of Probability, 10(4), 1088-1091.
  • [11] Kasprzak, W., Lysik, B. and Rybaczuk, M., (2004), Dimensions, Invariants Models and Fractals, Ukrainian Society on Fracture Mechanics, SPOLOM, Wroclaw-Lviv, Poland.
  • [12] Riza, M., Ozyapıcı, A. and Kurpınar, E., (2009), Multiplicative finite difference methods, Quarterly ¨ of Applied Mathematics, 67 (4), 745-754.
  • [13] Rybaczuk, M., Kedzia, A. and Zielinski, W., (2001), The concepts of physical and fractional dimensions II. The differential calculus in dimensional spaces, Chaos Solutions Fractals, 12, 2537-2552.
  • [14] Stanley, D., (1999), A multiplicative calculus, Primus, IX(4), 310-326.
  • [15] Volterra, V. and Hostinsky, B., (1938), Operations Infinitesimales Lineares, Herman, Paris.
Yıl 2013, Cilt: 3 Sayı: 1, 103 - 107, 01.06.2013

Öz

Kaynakça

  • [1] Aniszewska, D., (2007), Multiplicative Runge-Kutta method, Nonlinear Dynamics, 50, 265-272.
  • [2] Bashirov, A. E. and Bashirova, G., (2011), Dynamics of literary texts, Online Journal of Communication and Media Techniligies, 1 (3), 60-82.
  • [3] Bashirov, A. E., Kurpınar, E. and Ozyapıcı, A., (2008), Multiplicative calculus and its applications, ¨ Journal of Mathematical Analysis and Applications, 337 (1), 36-48.
  • [4] Bashirov, A. E., Kurpınar, E., Tandoˇgdu, Y. and Ozyapıcı, A., (2011), On modeling with multiplica- ¨ tive differential equations, Applied Mathematics - A Journal of Chinees Universities, 26(4), 425-438.
  • [5] Bashirov, A. E. and Riza, M., (2011), On complex multiplicative differentiation, TWMS Journal of Applied Engineering Mathematics, 1(1), 75-85.
  • [6] C´ordova-Lepe, F., (2006), The multiplicative derivative as a measure of elasticity in economics, TEMAT-Theaeteto Atheniensi Mathematica, 2(3), online.
  • [7] Daletskii, Yu. L. and Teterina, N. I., (1972), Multiplicative stochastic integrals, Uspekhi Matematicheskikh Nauk, 27(2:164), 167-168.
  • [8] Grossman, M. and Katz, R., (1972), Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA.
  • [9] Grossman, M., (1983), Bigeometric Calculus: A System with a Scale-Free Derivative, Archimedes Foundation, Rockport, MA.
  • [10] Karandikar, R. L., (1982), Multiplicative decomposition of non-singular matrix valued continuous semimartingales, The Annals of Probability, 10(4), 1088-1091.
  • [11] Kasprzak, W., Lysik, B. and Rybaczuk, M., (2004), Dimensions, Invariants Models and Fractals, Ukrainian Society on Fracture Mechanics, SPOLOM, Wroclaw-Lviv, Poland.
  • [12] Riza, M., Ozyapıcı, A. and Kurpınar, E., (2009), Multiplicative finite difference methods, Quarterly ¨ of Applied Mathematics, 67 (4), 745-754.
  • [13] Rybaczuk, M., Kedzia, A. and Zielinski, W., (2001), The concepts of physical and fractional dimensions II. The differential calculus in dimensional spaces, Chaos Solutions Fractals, 12, 2537-2552.
  • [14] Stanley, D., (1999), A multiplicative calculus, Primus, IX(4), 310-326.
  • [15] Volterra, V. and Hostinsky, B., (1938), Operations Infinitesimales Lineares, Herman, Paris.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Agamirza E. Bashirov Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 3 Sayı: 1

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