Bulletin of the Australian Mathematical Society

Research Article

On properties of semipreinvex functions

X. M. Yanga1, X. Q. Yang and K. L. Teoa2

a1 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

a2 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

Abstract

In this paper, we first discuss some basic properties of semipreinvex functions. We then show that the ratio of semipreinvex functions is semipreinvex, which extends earlier results by Khan and Hanson [6] and Craven and Mond [3]. Finally, saddle point optimality criteria are developed for a multiobjective fractional programming problem under semipreinvexity conditions.

(Received May 15 2003)

Correspondence:

p1 Current address:, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Horn, Kowloon, Hong Kong, e-mail: maxmyang@polyu.edu.hk and Department of Mathematics, Chongqing Normal University, Chongqing 40047m China