Generalized F-convexity and its classification

Abstract

Several types of F-convexity (FC), pseudo F-convexity (PFC) and quasi F-convexity (QFC) of a nonlinear function are described. Direct implications of the relations existing between various types of F-convexity and generalized F-convexity are presented as well as a block diagram has been proposed which depicts the implications reflected in this paper.

Keywords:

• (Fρ)-convexity
• Clarke's Generalized Directional Derivative
• Smooth and Nonsmooth Functions