Hadamard product of holomorphic mappings associated with the conic shaped domain

Authors : Syed Zakar HUSSAİN BUKHARİ, Aamir SHAHZAD

Pages : 105-117

Doi:10.31801/cfsuasmas.1061950

View : 15 | Download : 7

Publication Date : 2023-03-30

Article Type : Research Paper

Abstract :We define certain subclasses $\\delta-\\mathcal{UM}insert ignore into journalissuearticles values(\\ell,\\eta_{1},\\eta_{2});$ and $\\delta-\\mathcal{UM}_{\\Im}insert ignore into journalissuearticles values(\\ell,\\eta_{1},\\eta_{2});$ 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 $f\\in \\delta-\\mathcal{UM}insert ignore into journalissuearticles values(\\ell,\\eta_{1}% ,\\eta_{2});.$ We also discuss the characterization for $f\\in \\delta -\\mathcal{UM}_{\\Im}insert ignore into journalissuearticles values(\\ell,\\eta_{1},\\eta_{2});$ along with the coefficient bounds and other problems. Using certain conditions for functions in the class $\\delta-\\mathcal{UM}insert ignore into journalissuearticles values(\\ell,\\eta_{1},\\eta_{2});,$ we also define another class $\\delta-\\mathcal{UM}^{\\ast}insert ignore into journalissuearticles values(\\ell,\\eta_{1},\\eta_{2});$ and study some subordination related result.
Keywords : Caratheodory functions, convolution, subordination