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

Abdolreza Tehranchi, Ahmad Mousavi, M. Waghefi

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
$\mathbb{T}_{c}^{\delta}(\alpha,\beta).$

Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

Copyright © Canadian Center of Science and Education

To make sure that you can receive messages from us, please add the 'ccsenet.org' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.