Looks like some kind of Rhododendron Tina. I don't know too much about them so hopefully someone else will be along to help you out.
Thanks for id ing my plant. This plant is so wide that it takes up a lot of place in my tiny front yard.Can I cut a few branches now or will it prevent it from bearing flowers now that it is almost spring? Is there a special way in which I should cut them? There are a few branches in which a few of the leaves are turning black.What should I do about them? Thanks again. Tina
I think it may be either a dwarf rhododendron or, as the others have said, an Indian Hawthorn (Rhaphiolepis indica.) Maybe you could take another piccie when it flowers as the flowers will certainly help us to identify it. :-D
I would wait until after it flowers to trim it to the size you want. You will cut away all of your flower buds now. And please do post a pic when it is in bloom.
I'm going to second Cajunbelle now, The general rule for shaping or pruning spring blooming shrubs, is to wait until after they bloom, then shape them soon after, and that would be best for either Rhodies or Hawthorne.