A Class ofG-Semipreinvex Functions and Optimality

A class ofG-semipreinvex functions, which are some generalizations of the semipreinvex functions, and theG-convex functions, is introduced. Examples are given to show their relations amongG-semipreinvex functions, semipreinvex functions andG-convex functions. Some characterizations ofG-semipreinvex functions are also obtained, and some optimality results are given for a class ofG-semipreinvex functions. Ours results improve and generalize some known results.

On properties of semipreinvex functions

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.