Some Properties for Subordinations of Analytic Functions - Hatun Özlem Güney; Daniel Breaz; Shigeyoshi Owa (Axioms, 2023)
Let the class of functions of <semantics>f(z)</semantics> of the form <semantics>f(z)=z+<msubsup>∑k=2∞</msubsup>akzk</semantics>, which are denoted by <semantics>A</semantics> and called analytic functions in the open-unit disk. There are many interesting properties of the functions <semantics>f(z)</semantics> in the class <semantics>A</semantics> concerning the subordinations. Applying the three lemmas for <semantics>f(z)∈A</semantics> provided by Miller and Mocanu and by Nunokawa, we consider many interesting properties of <semantics>f(z)∈A</semantics> with subordinations. Furthermore, we provide simple examples for our results. We think it is very important to consider examples of the results.