On close-to-convex infinitesimal generators with fixed initial coefficient

Amani, Mostafa; Ebadian, Ali; Aghalary, Rasoul

doi:10.30495/maca.2024.720826

On close-to-convex infinitesimal generators with fixed initial coefficient

10.30495/maca.2024.720826

Volume 6, Issue 4
Autumn 2024

Pages 23-33

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

Mostafa Amani ^¶

Ali Ebadian ^¶

Rasoul Aghalary

Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran

Abstract

This article extends the subclasses of infinitesimal generators to $\mathcal{C}_{n,b}(\alpha)$ and $\mathcal{S}\mathcal{S}^*_{n,b}(\alpha)$ that are associated with close-to-convex and starlike functions with fixed second coefficient. The main result of this study is a solution to an open problem in a certain specific case.

Keywords

Close-to-convex

Fixed second coefficient

Mark-Strohhacker

Open problem

infinitesimal generator

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