Generalized (ρ,θ)-η-invexity and generalized (ρ,θ)-η-invariant-monotonicity

In this paper several kinds of (ρ,θ)-η-invariant-monotone functions and generalized (ρ,θ)-η-invariant-monotone functions are considered. For a given Frechet differentiable function f,∇f (gradient of f), (ρ,θ)-η-invariant-monotonicity of ∇f is related to (ρ,θ)-η-invexity of f. It is also shown that (ρ,θ)-η-invariant-monotonicity and generalized (ρ,θ)-η-invariant-monotonicity are proper generalizations of invariant-monotonicity and generalized invariant-monotonicity.