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

Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India
Nonlinear Analysis: Theory, Methods & Applications 01/2008; DOI:10.1016/j.na.2007.02.004

ABSTRACT 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.

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