p-Subordination chains and p-valence integral operators

Abstract

In the present investigation we obtain some sufficient conditions for the analyticity and the $p$-valence of an integral operator in the unit disk $\mathbb{D}$. Using these conditions we give some applications for a few different integral operators. The significant relationships and relevance to other results are also given. A number of known univalent conditions would follow upon specializing the parameters involved in our main results.