Study on Integral Operators by Using Komato Operator on a New Class of Univalent Functions

Abstract

Let $\mathbb{T}$ be the class of functions $ f(z)=z-\sum^\iny_{k=2} a_kz^k$
 which are analytic in the unit disk $U=\{z\in \mathbb{C}:|z|<1\}.$ By using Komato operator
 $\mathcal{K}^{\delta}_{c}(f)$, we introduce a new subclass
  $\mathbb{T}_{c}^{\delta}(\alpha,\beta)$, whose elemants satisfying
  in $$ Re\{\frac{\mathcal{K}^{\delta}_{c}(f)}{z[\mathcal{K}^{\delta}_{c}(f)]'}\}>\alpha|\frac{\mathcal{K}^{\delta}_{c}(f)}{z[\mathcal{K}^{\delta}_{c}(f)]'}-1|+\beta, $$
and we study linear combination and derive some interesting
properties for the class $\mathbb{T}_{c}^{\delta}(\alpha,\beta).$
Also, we study on some integral operators on
$\mathbb{T}_{c}^{\delta}(\alpha,\beta).$