1Department of Mathematics, Galgotia College of Engineering & Technology, Greater Noida, U.P-201301, India
2Professor of Eminence and Research Head, KIlT University, Bhubaneswar, Odisha-751024
3Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India
*Author for Correspondence. cnahak@maths.iitkgp.ernet.in
In this paper, we study the relations between ρ – (η, θ)-invexity and ρ – (η, θ)-monotonocity in a real Banach space X. Particularly, we establish the relations between ρ – (η, θ)-invexity, generalized ρ – (η, θ)-invexity and ρ – (η, θ)-pseudo-monotonocity, ρ – (η, θ)-quasi-monotonocity in X. Some examples are given which show that ρ – (η, θ)-monotone and ρ – (η, θ)-invexity are proper generalization of η-monotone and invexity.
ρ – (η, θ)-monotone, ρ – (η, θ)-invex function, Generalized ρ – (η, θ)-invex function, ρ – (η, θ)-pseudo-monotone, ρ – (η, θ)-quasi-monotone
