Here is a jsFiddle that demonstrates the process to have both a fixed sized using position:fixed in a outer div while an inner div holding the image is using background-size:contain.
EDIT: Now an extra div is used to include any border requirements too!
EDIT-2: Updated jsFiddle with :contain, not :cover along with non-abstract image.
For old browsers such as IE6-8 there are many plugins to choose from that allow the use of CSS3 Styles. This jQuery Plugin named backgroundSize.js is specifically for the use of :cover and :contain for background-size and is provided by SO member Louis-Rémi if you need that option.