A Generalized Class of k-Starlike Functions Involving a Calculus Operator

In this paper, involving a calculus operator I∼δ,ν,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \tilde{I}^{\delta ,\nu } , $$\end{document} a generalized class US(k,δ,ν)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\text{US}}(k,\delta ,\nu ) $$\end{document} of k-starlike functions is defined and an estimate for coefficients of functions belonging to this class is determined. For this class, coefficient inequality is given and is applied to find certain mappings of the operator I∼δ,ν,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \tilde{I}^{\delta ,\nu } , $$\end{document} under some parametric restrictions. Results based on inclusion property and convolution property, are also derived. Further, for a subclass US¯(k,δ,ν)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{\text{US}} (k,\delta ,\nu ) $$\end{document} of US(k,δ,ν),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\text{US}}(k,\delta ,\nu ), $$\end{document} results on bounds, extreme points and radius of starlikeness are obtained.