The Cauchy Theorems and Their Applications

Abstract

where $\gamma _0$ and $\gamma _1$ are closed paths in $\Omega$ such that they are $\Omega$-homotopic and $f\in H(\Omega ).$ This implies Theorem 1.6 with $f(z) = \frac{1}{z-a}$ such that $a \not \in \Omega .$ This also implies the Cauchy theorem for closed path in $\Omega$ such that it is null-homotopic in $\Omega .$