Applicable Multiplicative Calculus Using Multiplicative Modulus Function

Yıl 2019, Cilt: 2 Sayı: 2, 195 - 199, 20.12.2019

Ganesa Moorthy C.

https://doi.org/10.33401/fujma.630045

Öz

The classical calculus is viewed as additive calculus based on addition in the real line.  Another known multiplicative calculus corresponding to multiplication in the positive real axis has been precisely introduced.  Abstract multiplicative integration through positive measures has been newly introduced.  Results of multiplicative differentiation and integration have been obtained for completion, when some of them have been obtained through multiplicative modulus function. Results have been obtained also for abstract multiplicative measure integration.

Anahtar Kelimeler

Differentiation, Positive measure integration, Riemann integration

Destekleyen Kurum

RUSA-Phase 2.0 grant

Proje Numarası

letter No.F 24-51/2014-U, Policy (TN Multi-Gen),

Teşekkür

Dr. C. Ganesa Moorthy (Professor, Department of Mathematics, Alagappa University, Karaikudi- 630003, INDIA) gratefully acknowledges the joint financial support of RUSA-Phase 2.0 grant sanctioned vide letter No.F 24-51/2014-U, Policy (TN Multi-Gen), Dept. of Edn. Govt. of India, Dt. 09.10.2018, UGC-SAP (DRS-I) vide letter No.F.510/8/DRS-I/2016 (SAP-I) Dt. 23.08.2016 and DST (FIST - level I) 657876570 vide letter No.SR/FIST/MS-I/2018-17 Dt. 20.12.2018.

Kaynakça

• [1] A. E. Bashirov, E. M. Kurpinar, A. Ozyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl., 337 (2008), 36-48.
• [2] C. G. Moorthy, Infinite products using multiplicative modulus function, Math. Student, 88(3&4) (2019), 39-54.
• [3] M. Grossman, R. Katz, Non-Newtonian Calculus, Les Press, Pigeon Cove, MA, 1972.
• [4] U. Kadak, M. Ozl¨uk, Generalized Runge-Kutta method with respect to nonNewtonian calculus, Abst. Appl. Anal., (2015), Article ID 594685, 10 pages.
• [5] A. Uzer, Multiplicative type complex calculus as an alternative to the classical calculus, Comput. Math. Appl., 60 (2010), 2725-2737.
• [6] N. Yalcin, E. Celik, A. Gokdogan, Multiplicative Laplace transform and its applications, Optik, 127(20) (2016), 9984-9995.
• [7] T. Abadeljawad, On multiplicative fractional calculus, (2015), arXiv:1510.04176v1[math.CA].
• [8] D. Aniszewska, Multiplicative Runge-Kutta method, Non-Linear Dyn., 50(2007), 265-272.
• [9] A. E. Bashirov, E. Misirli, Y. Tandogdu, A. Ozyapici, On modelling with multiplicative differential equations, Appl. Math. J. Chinese Univ., 26(4)(2011), 425-428.
• [10] A. E. Bashirov, M. Riza, Complex multiplicative calculus, (2011), arXiv:1103.1462[math.CV].
• [11] A. E. Bashirov, M. Riza, On complex multiplicative differentiation, TWMS J. App. Eng. Math., 1(1) (2011)75-85.
• [12] A. E. Bashirov, E. M. Kurpinar, A. Ozyapici, Multiplicative Calculus and its applications, J. Math. Anal. Appl., 337 (2008), 36-48.
• [13] A. E. Bashirov, S. Norozpour, On an alternative view to complex calculus, Math. Meth. Appl. Sci., 41 (2018), 7313-7324.
• [14] A. H. Bhat, J. Majid, I. A. Wani, Multiplicative Sumudu transform and its applications, J. Emerging Tech. Innovative Res., 6(1)(2019), 579-589.
• [15] K. Boruah, B. Hazarika, Application of geometric calculus in numerical analysis and difference sequence spaces, J. Math. Anal. Appl., 449(2)(2017),1265-1285.
• [16] K. Boruah, B. Hazarika, G-Calculus, TWMS J. Appl. Eng. Math., 8(1) (2018), 94-105.
• [17] K. Boruah, B. Hazarika, Bigeometric integral calculus, TWMS J. Appl. Eng. Math., 8(2) (2018), 374-385.
• [18] K. Boruah, B. Hazarika, A. E. Bashirov, Solvability of bigeometric differential equations by numerical methods, Bol. Soc. Paran. Mat. (in press).
• [19] D. Filip, C. Piatecki, An overview on the non-Newtonian calculus and its applications to economics, Appl. Math. Comput., 187(1) (2007), 68-78.
• [20] L. Florack, H. Assen, Multiplicative calculus in biomedical image analysis, J. Math. Imaging Vis., 42 (2012), 64-75.
• [21] D. Stanley, A multiplicative calculus, Primus, 9(4) (1999), 310-326.
• [22] E. J. P. G. Schmidt, On multiplicative Lebesgue integration and families of evolution operators, Math. Scand., 29 (1971), 113-133.
• [23] W. Rudin, Principles of Mathematical Analysis, Third edition, McGraw Hill, London, 1976.
• [24] W. Rudin, Real and Complex Analysis, Third edition, McGraw Hill, New York, 1987.
• [25] N. Marikkannan, P. Sooriyakala, C. G. Moorthy, Certain applications of differential subordination and superordination, Int. J. Pure Appl. Math., 34(4) (2007), 547-558.
• [26] N. Marikkannan, C. G. Moorthy, On applications of differential subordination and superordination, Tamkang J. Math., 39(2) (2008), 155-164.
• [27] C. G. Moorthy, Measure theory and Hausdorff dimension of Cantor sets of Continued fractions, Ph.D. Thesis, Alagappa University, 1992.
• [28] C. G. Moorthy, N. Marikkannan, M. P. Jeyaraman, Applications of differential subordination and superordination, J. Indones. Math. Soc., 14(1) (2012), 47-56.
• [29] C. G. Moorthy, R. Vijaya, P. Venkatachalapathy, Hausdorff dimension of Cantor-like sets, Kyungpook Math. J., 32(2) (1992), 197-202.
• [30] C. G. Moorthy, A problem of good on Hausdorff dimension, Mathematika, 39(2) (1992), 244-246.