Hi,
as already pointed out, you need a special geometry for that with the correct UVs.
Also the mapping must match your fisheye effect as fisheye is a pretty general word - it mostly means catching an unusually high angle.
A special case is a hemisphere map, where you have an angle of 180°. That is easy to map. I've attached an example for that special case.
With your sample picture it won't look perfect. With a hemispherical map it does. You could fetch such an image from the web to try it in the attached scene. For instance
this picture.
cheers,
rou