I really hope I possibly could clearly described it here,

I've got a web applications let us say it's www.mywebapps.com/user_title

the user are thinking about creating a website reputation for themself like www.user_title.internet and also the access is going to be show what in www.mywebapps.com/user_title

so forexample www.mywebapps.com/user_title/show/1 it might be accessible from www.user_title.internet/show/1 too

how to do this task ? is it feasible ?

The consumer must first register the domain!

You may not mean a subdomain ?
Like user-title.mywebapps.com (underscores aren't legal in domains)

In either case you need to use mod_rewrite.

Subdomains tend to be simpler than recently registered names because you will have to customize the webserver for every title. for just a couple of thats simple for may that's hard. For any subdomain its just a wildcard along with a mod_rewrite command either in the virtual hosts config or even the .htaccess file without having accessibility virtual hosts config

Electricity

You will have to add the domain for your virtual hosts configuration. the simplest way could be produce a new virtualhost for every new customers domain title. Then set the documentroot to that particular customers subfolder.

For instance when the documentroot for that primary website is

/home/mywebapps/public_html

Then within the customers virtual host provide a document cause of

/home/mywebapps/public_html/username

This is acceptable for a static or simple site. for any more complicated dynamic site you might be better of utilizing mod_rewrite.

Electricity

You would need to pay to join up the domain title each time. And wait for a title to propagate with the DNS servers, which could require sometime.

You may rather take a look at using subdomains - something similar to user_name.mywebapps.com

Take a look at Apache support for virtual hosts:

http://httpd.apache.org/docs/1.3/vhosts/

But clearly you have to register the domains preferred (Apache will not like magic do this for you personally :-)

Take a look in the mod_vhost_alias module. You'll handle in a single configuration file all of the Virtualhosts, with variables for DocumentRoot and ServerName. So with this particular module you are able to map the DocumentRoot of every title based virtualhost on each home user directory.