ON COMPLEX MULTIPLICATIVE INTEGRATION

• Main Authors: AGAMIRZA E. BASHIROV, SAJEDEH NOROZPOUR
• Format: Article
• Language: English
• Published: Isik University 2017-06-01
• Series: TWMS Journal of Applied and Engineering Mathematics
• Subjects: complex calculus; complex integral; multiplicative calculus
• Online Access: http://jaem.isikun.edu.tr/web/index.php/current/93-vol7no1/281-on-complex-multiplicative-integration

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