An open circuited stub looks somewhat like a series connection of an L & C to ground.  You can vary the impedance and width of the stub to approximate most L-C combinations.  Can use in elliptical lowpass or highpass filters.  The only problem, or benefit depending on how you look at it, is that the OC stub looks like a short circuit at whatever frequency it is quarterwave at.

is that means that the grounded point for a quarter wave resonator can replaced by a stub?

i have simulate my 4th order filter design which consists of two half-wave resonators and two quarter-wave resonators, where i have replaced the grounded point of the quarter wave resonator by a stub, but the frequency response doesn't seem to be a 4th order band pass filter, it only have 2 peaks on the frequency response, is that because of i'm using the stub?

What type of filter are you making?  Lowpass, Highpass, Bandpass, etc?

i'm designing a bandpass filter for centre frequency of 2GHz and bandwidth of 500MHZ

does the stub can act as a k-inverter in the bandpass filter?

For this type of filter I would use a stub that is short circuited on one end, and approximately 90 degrees long at 2 GHz.  I would also recommend 3 or 5 or some other odd number of stubs.  4 stubs = 4 resonators which inherently will not match a 50 ohm input to a 50 ohm output, causing all sorts of ripple problems.  

i don't actually get what you mean by using odd numbers of stub. is that means that i have to apply the stub on each resonator? it's hardfor me to explain my design in words, do you mind giving me your email address so that i can show you my design?
as for the stub, i'm actually replaced the short circuit point of the quarter wave resonator by a stub, so why should I use the stub that short circuited on one end?

and in a matter of determining the external coupling coefficient, when i remocv the short circuited point on one end of the resonator and connect to the input feedline, the resonant frequency will rise up to 2500MHz as the grounded point has been remove, so is it a must that i have to get a resonant frequency of 2GHz by varying the size of the resonator in order to determine the external coupling coefficient?

No, I did not mean to replace your ground with a stub.  You could do that, but a stub does not look like a good ground over a range of frequencies, but only at one frequency.  So a filter that replaces grounds with stubs would not work very well.

I am sure there are some unique applications where you replace a ground with a stub to form a specific elliptical function filter, but that is a little more advanced than what you seem to need.

I mean to use shorted quarterwave stubs AS the resonators in a bandpass filter.  I whipped up one quickly, but the internal impedances got a little big, so give me a few days to get back to it, and I will publish a design that will work and be realizable.

As far as emails, I am willing, but the moderators of this board do not want emails listed in messages.  They yelled at me once, so unless you can figure out how to send a personal message, I guess this is all we can do.