Generalized invex monotonicity

In this paper the generalized invex monotone functions are defined as an extension of monotone functions. A series of sufficient and necessary conditions are also given that the related generalized invexity of the function θ with the generalised invex monotonicity of its gradient ∇θ. This new class of functions will be important in order to characterize the solutions of the Variational-like Inequality Problem and Mathematical Programming Problem.