The Faber polynomial expansion method and its application to the general coefficient problem for some subclasses of bi-univalent functions associated with a certain q-integral operator

By Hari M. Srivastava, Shahid Khan, Qazi Zahoor Ahmad, Nazar Khan, S. Hussain. Studia Universitatis Babeş-Bolyai. Mathematica, 2018

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In our present investigation, we first introduce several new subclasses of analytic and bi-univalent functions by using a certain $q$-integral operator in the open unit disk $$\mathbb{U}=\{z: z\in \mathbb{C} \quad \text{and} \quad \left \vert z\right \vert <1\}.$$ By applying the Faber polynomial expansion method as well as the $q$-analysis, we then determine bounds for the $n$th coefficient in the Taylor-Maclaurin series expansion for functions in each of these newly-defined analytic and bi-univalent function classes subject to a gap series condition. We also highlight some known consequences of our main results.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4874e350be688db992a40ca0ecd8e2cd2dd0d1a5

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Applications of a certain $q$-integral operator to the subclasses of analytic and bi-univalent functions (2021, methodology): “[45] introduced the q-version of the Noor integral operator as follows.”