- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 72 Issue: 1
- Hadamard product of holomorphic mappings associated with the conic shaped domain
Hadamard product of holomorphic mappings associated with the conic shaped domain
Authors : Syed Zakar Hussain Bukhari, Aamir Shahzad
Pages : 105-117
Doi:10.31801/cfsuasmas.1061950
View : 10 | Download : 4
Publication Date : 2023-03-30
Article Type : Research
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