The second mean value theorem for complex line integral

Abstract

In real iterations, several types of mean value theorems for definite integrals are used. In complex domain, we cannot specifically formulate the mean value theorem of a particular complex line integral (L) ∫f(z)dz , since we are unable to give an appropriate geometric interpretation of the integral over the surface below a curve L (from z0 to z1 ). Based on the mean value theorems for a complex line integral in [Vujakovic J., The mean value theorem of line complex integral and Sturm function. Applied Mathematical Sciences 2014; 8 (37): 1817-1827.], we got the idea to formulate the second mean value theorem in complex domain for the product of two analytic functions.