Hadamard product of holomorphic mappings associated with the conic shaped domain

Year 2023, , 105 - 117, 30.03.2023

Syed Zakar Hussain Bukhari , Aamir Shahzad

https://doi.org/10.31801/cfsuasmas.1061950

Abstract

We define certain subclasses $\delta-\mathcal{UM}(\ell,\eta_{1},\eta_{2})$ and
$\delta-\mathcal{UM}_{\Im}(\ell,\eta_{1},\eta_{2})$ of holomorphic mappings
involving some differential inequalities. These functions are actually
generalizations of some basic families of starlike and convex mappings. We
study sufficient conditions for $f\in \delta-\mathcal{UM}(\ell,\eta_{1}%
,\eta_{2}).$ We also discuss the characterization for $f\in \delta
-\mathcal{UM}_{\Im}(\ell,\eta_{1},\eta_{2})$ along with the coefficient bounds
and other problems. Using certain conditions for functions in the class
$\delta-\mathcal{UM}(\ell,\eta_{1},\eta_{2}),$ we also define another class
$\delta-\mathcal{UM}^{\ast}(\ell,\eta_{1},\eta_{2})$ and study some
subordination related result.

Keywords

Caratheodory functions, convolution, subordination

Supporting Institution

N/A

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