ON COMPLEX MULTIPLICATIVE INTEGRATION

NOROZPOUR, SAJEDEH; BASHIROV, AGAMIRZA E.

ON COMPLEX MULTIPLICATIVE INTEGRATION

AGAMIRZA E. BASHIROV, (Eastern Mediterranean University, Gazimagusa, North Cyprus)

SAJEDEH NOROZPOUR (Institute of Control Systems, ANAS, Baku, Azerbaijan)

TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics

0 0

Yıl: 2017 Cilt: 7 Sayı: 1 Sayfa Aralığı: 82 - 93 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

ON COMPLEX MULTIPLICATIVE INTEGRATION

Öz:

In the present paper, we extend the multiplicative integral to complex-valuedfunctions of complex variable. The main difficulty in this way, that is, the multi-valuednature of the complex logarithm is avoided by division of the interval of integration to afinite number of local intervals, in each of which the complex logarithm can be localizedin one of its branches. Interestingly, the complex multiplicative integral became a multivalued function. Some basic properties of this integral are considered. In particular, it isproved that this integral and the complex multiplicative derivative are bonded in a kindof fundamental theorem.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Ahlfors,L.V., (1979), Complex Analysis, 3rd ed., McGraw-Hill, New York.
[2] Bashirov,A.E., (2013), On line and double multiplicative integrals, TWMS Journal of Applied and Engineering Mathematics, 3(1), 103-107.
[3] Bashirov,A.E. and Bashirova,G., (2015), Literature as a diffusion process, in: Brownian Motion: Elements, Dynamics and Applications, Editors: M.A. McKibben and M. Webster, Nova Science Publications, pp. 201-218.
[4] Bashirov,A.E., Kurpınar,E., and Ozyapıcı,A., (2008), Multiplicative calculus and its applications, ¨ Journal of Mathematical Analysis and Applications, 337(1), 36-48.
[5] Bashirov,A.E., Mısırlı,E., Tando?gdu,Y., and Ozyapıcı,A., (2011), On modeling with multiplicative ¨ differential equations, Applied Mathematics - Journal of Chinese Universities, 26(4), 425-438.
[6] Bashirov,A.E. and Riza,M., (2011), On complex multiplicative differentiation, TWMS Journal of Applied and Engineering Mathematics, 1(1), 51-61.
[7] C´ordova-Lepe,F., (2006), The multiplicative derivative as a measure of elasticity in economics, TEMAT-Theaeteto Atheniensi Mathematica, 2(3), online.
[8] C´ordova-Lepe,F. and Pinto,M., (2009), From quotient operation toward a proportional calculus, International Journal of Mathematics, Game Theory and Algebra, 18(6), 527-536.
[9] Daletskii,Yu.L. and Teterina,N.I., (1972), Multiplicative stochastic integrals, Uspekhi Matematicheskikh Nauk, 27(2:164), 167-168.
[10] Florack,L. and Van Assen,H., (2011), Multiplicative calculus in biomedical image analysis, Journal of Mathematical Imaging and Vision, doi: 10.1007/s10851-011-0275-1.
[11] Greene,R.E. and Krantz,S.G., (2006), Function Theory of One Complex Variable, 3rd ed., AMS, Providence, RI.
[12] Grossman,M., (1983), Bigeometric Calculus: A System with a Scale-Free Derivative, Archimedes Foundation, Rockport, MA.
[13] Grossman,M. and Katz,R., (1972), Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA.
[14] Karandikar,R.L., (1982), Multiplicative decomposition of non-singular matrix valued continuous semimartingales, The Annals of Probability, 10(4), 1088-1091.
[15] Mısırlı,E. and G¨urefe,Y., (2011), Multiplicative Adams Bashforth-Moulton methods, Numerical Algorithms, 57(4), 425-439.
[16] Ozyapıcı,A., Riza,M., Bilgehan,B., and Bashirov,A.E., (2014), On multiplicative and Volterra mini- ¨ mization method, Numerical Algorithms, 67(3), 623-636.
[17] Ozyapıcı,A. and Bilgehan,E., (2016), Finite product representation via multiplicative calculus and its ¨ applications to exponential signal processing, Numerical Algorithms, 71(2), 475-489.
[18] Riza,M., Ozyapıcı,A., and Kurpınar,E., (2009), Multiplicative finite difference methods, ¨ Quarterly of Applied Mathematics, 67(4), 745-754.
[19] Sarason,D., (2007), Complex Functions Theory, AMS, Providence, RI.
[20] Stanley,D., (1999), A multiplicative calculus, Primus, IX(4), 310-326.

APA	BASHIROV A, NOROZPOUR S (2017). ON COMPLEX MULTIPLICATIVE INTEGRATION. , 82 - 93.
Chicago	BASHIROV AGAMIRZA E.,NOROZPOUR SAJEDEH ON COMPLEX MULTIPLICATIVE INTEGRATION. (2017): 82 - 93.
MLA	BASHIROV AGAMIRZA E.,NOROZPOUR SAJEDEH ON COMPLEX MULTIPLICATIVE INTEGRATION. , 2017, ss.82 - 93.
AMA	BASHIROV A,NOROZPOUR S ON COMPLEX MULTIPLICATIVE INTEGRATION. . 2017; 82 - 93.
Vancouver	BASHIROV A,NOROZPOUR S ON COMPLEX MULTIPLICATIVE INTEGRATION. . 2017; 82 - 93.
IEEE	BASHIROV A,NOROZPOUR S "ON COMPLEX MULTIPLICATIVE INTEGRATION." , ss.82 - 93, 2017.
ISNAD	BASHIROV, AGAMIRZA E. - NOROZPOUR, SAJEDEH. "ON COMPLEX MULTIPLICATIVE INTEGRATION". (2017), 82-93.

APA	BASHIROV A, NOROZPOUR S (2017). ON COMPLEX MULTIPLICATIVE INTEGRATION. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 7(1), 82 - 93.
Chicago	BASHIROV AGAMIRZA E.,NOROZPOUR SAJEDEH ON COMPLEX MULTIPLICATIVE INTEGRATION. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics 7, no.1 (2017): 82 - 93.
MLA	BASHIROV AGAMIRZA E.,NOROZPOUR SAJEDEH ON COMPLEX MULTIPLICATIVE INTEGRATION. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, vol.7, no.1, 2017, ss.82 - 93.
AMA	BASHIROV A,NOROZPOUR S ON COMPLEX MULTIPLICATIVE INTEGRATION. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics. 2017; 7(1): 82 - 93.
Vancouver	BASHIROV A,NOROZPOUR S ON COMPLEX MULTIPLICATIVE INTEGRATION. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics. 2017; 7(1): 82 - 93.
IEEE	BASHIROV A,NOROZPOUR S "ON COMPLEX MULTIPLICATIVE INTEGRATION." TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 7, ss.82 - 93, 2017.
ISNAD	BASHIROV, AGAMIRZA E. - NOROZPOUR, SAJEDEH. "ON COMPLEX MULTIPLICATIVE INTEGRATION". TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics 7/1 (2017), 82-93.