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Advances in Operations Research
Volume 2009, Article ID 381831, 10 pages
Research Article

On Properties of Geodesic 𝜂 -Preinvex Functions

1Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
2Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 30 October 2008; Revised 19 February 2009; Accepted 5 March 2009

Academic Editor: Hsien-Chung Wu

Copyright © 2009 I. Ahmad et al. 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.


The present paper deals with the properties of geodesic 𝜂 -preinvex functions and their relationships with 𝜂 -invex functions and strictly geodesic 𝜂 -preinvex functions. The geodesic 𝜂 -pre-pseudo-invex and geodesic 𝜂 -pre-quasi-invex functions on the geodesic invex set are introduced and some of their properties are discussed.