Generalized image-invexity and generalized image-invariant-monotonicity Original Research Article

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