International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 8, Pages 1253-1276

Generalized (𝔉,b,ϕ,ρ,θ)-univex n-set functions and global parametric sufficient optimality conditions in minmax fractional subset programming

G. J. Zalmai

Department of Mathematics and Computer Science, Northern Michigan University, Marquette 49855, MI, USA

Received 28 December 2003; Revised 3 October 2004

Copyright © 2005 G. J. Zalmai. 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.


We first define a new class of generalized convex n-set functions, called (𝔉,b,ϕ,ρ,θ)-univex functions, and then establish a fairly large number of global parametric sufficient optimality conditions under a variety of generalized (𝔉,b,ϕ,ρ,θ)-univexity assumptions for a discrete minmax fractional subset programming problem.