Generalized convexity and generalized monotonocity

Abstract

General definitions of monotonocity, quasimonotonocity, pseudomonotonocity and strong monotonocity of a vector valued function defined on a subset of an n-dimensional Euclidean space are given. Some properties and characterizations are studied in the genera] setting. A relationship between generalized monotonocity and (Φ₁, Φ₂)– convexity introduced earlier by the authors, is described under certain conditions. Applications of the general definitions are studied in terms of invexity and B-vexity.