Indian Journal of Industrial and Applied Mathematics
  • Year: 2012
  • Volume: 3
  • Issue: 1Special

Generalized ρ–(η, θ)-Invexity and Generalized ρ–(η, θ)-Monotonocity

  • Author:
  • N. Beherat1,, C. Nahak3,, S. Nanda2,
  • Total Page Count: 13
  • Published Online: Jun 1, 2012
  • Page Number: 74 to 86

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

**snanda@maths.iitkgp.ernet.in

***narmda.behera@ga1gotiacollege.edu.

Abstract

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.

Keywords

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