A question in Bazaraa's book

I am working on a problem which is similar to a question in Bazaraa's book, Nonlinear Programming(Question 3.61, 3rd edition). If I solve that question, my problem is solved as well. The question is as follows:

Let g: S->R and h:S->R, where S is a nonempty convex set in R^n. Consider the function f: S->R defined by f(x)=g(x)/h(x). Show that f is quasiconvex if the following two conditions hold true:
a. g is convex on S, and g(x)>=0 for each x in S
b. h is concave on S, and h(x)>0 for each x in S.

Jinjing, NaC1, and 皆兄弟也, do you have any thought? Thanks in advance.

所有跟帖： 

• 回複：A question in Bazaraa's book -亂彈- ♂ (170 bytes) () 09/09/2010 postreply 18:23:20

• 回複：回複：A question in Bazaraa's book -guest1000- ♂ (24 bytes) () 09/10/2010 postreply 18:04:29

• First time See Quasi-Convex and It's Definition. -Commentate- ♂ (0 bytes) () 09/10/2010 postreply 19:23:58

• 不鼓勵給別人做作業 -badminton- ♂ (0 bytes) () 09/12/2010 postreply 17:39:37

• Thank you, I just back home, 亂彈is senior Mathematician -jinjing- ♀ (135 bytes) () 09/09/2010 postreply 19:32:06

• 回複：多謝你的邀請。我最多是個數學愛好者，很不專業。 -NaCl- ♂ (0 bytes) () 09/09/2010 postreply 20:05:18

• It's too professional, I never involved in it. Sorry! -皆兄弟也- ♂ (0 bytes) () 09/10/2010 postreply 07:48:54