Vector optimization over cones involving support functions using generalized (Φ,ρ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\Phi ,\rho )$$\end{document}-convexity

In this paper we introduce new classes of cone-(Φ,ρ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\Phi ,\rho )$$\end{document}-convex functions which extend several generalized convexity notions introduced in the literature. We then employ the defined functions to study optimality and duality results for a vector optimization problem over cones involving support functions. A numerical example is given to illustrate the notions introduced and the results proved.