Journal of Applied Mathematics and Stochastic Analysis 
Volume 2006 (2006), Article ID 12736, 13 pages
doi:10.1155/JAMSA/2006/12736

Generalized preinvex functions and their properties

Muhammad Aslam Noor and Khalida Inayat Noor

 Department of Mathematics, COMSATS Institute of Information Technology, Plot 30, Sector H-8, Islamabad, Pakistan
Received 9 January 2005; Revised 9 August 2005; Accepted 2 September 2005

Abstract

We introduce some new classes of preinvex and invex functions, which are called ϕ-preinvex and ϕ-invex functions. We study some properties of these classes of ϕ-preinvex (ϕ-invex) functions. In particular, we establish the equivalence among the ϕ-preinvex functions, ϕ-invex functions, and ϕη-monotonicity of their differential under some suitable conditions.