G-CALCULUS

Yıl 2018, Cilt: 8 Sayı: 1, 94 - 105, 01.06.2018

K. Boruah B. Hazarika

Öz

Based on M. Grossman in [13] and Grossman an Katz [12], in this paper we prove geometric Rolle's theorem, Taylor's theorem, Mean value theorem. Also, we discuss about the properties and applications of bigeometric calculus.

Anahtar Kelimeler

Geometric real numbers, geometric arithmetic, bigeometric derivative.

Kaynakça

• A.E. Bashirov, M. Rıza, On Complex multiplicative differentiation, TWMS J. App. Eng. Math. (1)(2011) 75-85.
• A. E. Bashirov, E. Mısırlı, Y. Tandoˇgdu, A. ¨Ozyapıcı, On modeling with multiplicative differential equations, Appl. Math. J. Chinese Univ. 26(4)(2011) 425-438.
• A. E. Bashirov, E. M. Kurpınar, A. ¨Ozyapici, Multiplicative Calculus and its applications, J. Math. Anal. Appl. 337(2008) 36-48.
• Khirod Boruah and Bipan Hazarika, Application of Geometric Calculus in Numerical Analysis and Difference Sequence Spaces, arXiv:1603.09479v1, 31 May 2016.
• Khirod Boruah and Bipan Hazarika, Some basic properties of G-Calculus and its applications in numerical analysis, arXiv:1607.07749v1, 24 July 2016.
• A. F. C¸ akmak, F. Ba¸sar, On Classical sequence spaces and non-Newtonian calculus, J. Inequal. Appl. , Art. ID 932734, 12pages.
• A.F. C¸akmak and F. Ba¸sar, Certain spaces of functions over the field of non-Newtonian complex numbers, Abstr. Appl. Anal. 2014(2014), Article ID 236124, 12 pages.
• A.F. C¸akmak and F. Ba¸sar, On line and double integrals in the non-Newtonian sense, AIP Conference Proceedings, 1611(2014) 415-423.
• A.F. C¸akmak and F. Ba¸sar, Some sequence spaces and matrix transformations in multiplicative sense, TWMS J. Pure Appl. Math. 6(1)(2015) 27-37.
• Duff Campbell, Multiplicative Calculus and Student Projects, Department of Mathematical Sciences, United States Military Academy, West Point, NY,10996, USA.
• Michael Coco, Multiplicative Calculus, Lynchburg College. M. Grossman, R. Katz, Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts, 1972.
• M. Grossman, Bigeometric Calculus: A System with a scale-Free Derivative, Archimedes Foundation, Massachusetts, 1983.
• M. Grossman, An Introduction to non-Newtonian calculus, Int. J. Math. Educ. Sci. Technol. (4)(1979) 525-528.
• Jane Grossman, M. Grossman, R. Katz, The First Systems of Weighted Differential and Integral Calculus, University of Michigan, 1981.
• Jane Grossman, Meta-Calculus: Differential and Integral, University of Michigan, 1981.
• U. Kadak and Muharrem ¨Ozl¨uk, Generalized Runge-Kutta method with respect to non-Newtonian calculus, Abst. Appl. Anal., 2015 (2015), Article ID 594685, 10 pages.
• M. Riza and H. Akt¨ore, The Runge-Kutta Method in Geometric multiplicative Calculus. LMS J. Com- put. Math. 18(1)(2015) 539 - 554.
• W.F. Samuelson, S.G. Mark, Managerial Economics, Seventh Edition, 2012.
• D. Stanley, A multiplicative calculus, Primus IX 4 (1999) 310-326.
• S. Tekin, F. Ba¸sar, Certain Sequence spaces over the non-Newtonian complex field, Abstr. Appl. Anal. (2013). Article ID 739319, 11 pages.
• Cengiz T¨urkmen and F. Ba¸sar, Some Basic Results on the sets of Sequences with Geometric Calculus, Commun. Fac. Fci. Univ. Ank. Series A1. 61(2)(2012) 17-34.
• A. Uzer, Multiplicative type Complex Calculus as an alternative to the classical calculus, Comput. Math. Appl. 60(2010) 2725-2737.