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ON LINE AND DOUBLE MULTIPLICATIVE INTEGRALS

Year 2013, Volume 3, Issue 1, 103 - 107, 01.06.2013

Abstract

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.

References

  • [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.

Year 2013, Volume 3, Issue 1, 103 - 107, 01.06.2013

Abstract

References

  • [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.

Details

Primary Language English
Journal Section Research Article
Authors

Agamirza E. BASHİROV This is me
Department of Mathematics, Eastern Mediterranean University, Gazimagusa - North Cyprus

Publication Date June 1, 2013
Published in Issue Year 2013, Volume 3, Issue 1

Cite

Bibtex @ { twmsjaem761699, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2013}, volume = {3}, number = {1}, pages = {103 - 107}, title = {ON LINE AND DOUBLE MULTIPLICATIVE INTEGRALS}, key = {cite}, author = {Bashirov, Agamirza E.} }