You are going to have to be a lot more specific. OSX 10.4.11 is the highest in the 10.4 series. There are no system updates after that. There are upgrades (you have to buy them) but those take you to Leopard 10.5
There hasn't been an iTunes update for Tiger OS in several years. All iTunes updates and upgrades in the past year or two have required OSX 10.6 at least. For that you need an Intel based Mac. As far as Tiger OS is concerned, iTunes 9 was the last version. iTunes is currently on version 11.
You are being too uninformative for us to provide any real suggestions. You will have to tell us exactly what you want to update and why, which exact model computer you have. For example, yes you have 10.4.11 but if it is a PPC Mac then you can only go to 10.5, if it's an Intel Mac you can go higher but how high depends upon the exact model Mac (you don't say anything about your actual computer).
* Mac computer with an Intel, PowerPC G5, or PowerPC G4 (867MHz or faster) processor
minimum system requirements
* 512MB of memory (I say 1.5GB for PPC at least, 2-3GB minimum for IntelMacs)
* DVD drive for installation
* 9GB of available disk space (I say 30GB at least)
Classic/OS9 Apps no longer supported.
Trouble is Apple no longer sells it, check eBay & such for the Retail version, not the Gray Discs...
There are workarounds if the 867MHz CPU is the only hangup...
So we know more about it...
At the Apple Icon at top left>About this Mac, report the version of OSX from that window, then click on More Info, then click on Hardware> and report this upto but not including the Serial#...
Model Name: eMac
Model Identifier: PowerMac6,4
Processor Name: PowerPC G4 (1.2)
Processor Speed: 1.42 GHz
Number Of CPUs: 1
L2 Cache (per CPU): 512 KB
Memory: 2 GB
Bus Speed: 167 MHz
Boot ROM Version: 4.9.2f1
Just note that Leopard (OSX 10.5) itself is no longer supported and there are no more updates. I can't remember exactly when Apple dropped iTunes support for Leopard but I think it was early in iTunes 10. Apple nominally stops supporting system versions more than two generations old (so they stopped supporting OSX 10.4 when 10.6 came out -- they are now on 10.9). With iTunes tthey are a bit better and take it a step farther back and I believe iTunes 11 still runs on OSX 10.6, but not anything older. You can't go higher than OSX 10.5.8 with a PPC Mac.
If the unrevealed purpose behind this topic is you need the newest version of iTunes because you have a new Apple i-gadget such as a phone that requires new iTunes you are out of luck. Apple devices require the version of iTunes that is current when the device is being sold and there is no way you can get iTunes 11 to run on a PPC Mac.