International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2006 / Article

Open Access

Volume 2006 |Article ID 012736 | https://doi.org/10.1155/JAMSA/2006/12736

Muhammad Aslam Noor, Khalida Inayat Noor, "Generalized preinvex functions and their properties", International Journal of Stochastic Analysis, vol. 2006, Article ID 012736, 13 pages, 2006. https://doi.org/10.1155/JAMSA/2006/12736

Generalized preinvex functions and their properties

Received09 Jan 2005
Revised09 Aug 2005
Accepted02 Sep 2005
Published06 Apr 2006

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.

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Copyright © 2006 Muhammad Aslam Noor and Khalida Inayat Noor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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