Let f be a real differentiable function defined on the open subset A of Rn; f is said to be invex if the following inequality is satisfied f(x)-f(y)≥∇f(y)η(x,y),x,y∈A for a suitable function η. The purpose of this paper is to investigate the relationship between invexity and generalized convexity; moreover, necessary and sufficient conditions shall be given for a differentiable function to be η-invex, which are natural extensions of the analogous conditions for convex functions.
