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When you try to go browse to example.com and www.example.com, do you get different pages, or are they both your site (replace example.com with your domain)? Also, there are various search engine simulators available - I can't think of any, but a Google search should turn up a few. These should show you what Google, et al, see when they spider your site. It sounds like the host is incorrectly configured, but that's just a guess.
Chad
But sometimes when I type in www.mywesite.com com in goole search box I get result of my own website.
I need to know if I change my hosting company will this problem be solved. Or any other suggestions….
1 do a whois on your domain and check it is all correct and in your name
2 use ftp to your site and providing good ftp programme you should be able to view page as it is also then check source to see if some form of redirrect is added
3 ping your site and check what ip resolves to
4 open your site with the ip address in browser and see what that gives
sorry only suggestions and not sure if they will help best of luck
steve