Yes and no.

Classical era art was obviously very evident, and is a large majority of what the Renaissance 'was all about', we can see this with the marble statues resurging such as Michelangelo's 'David'.

In terms of Islamic art, again some aspects were prevalent in the Renaissance period of time, we see this with people such a Giotto who were famous for their frescos, most notably that of 'Life of St.Francis, Church of Assisi'. These Renaissance style frescos incorporated classical era style painting with the proportions of humanistic aspects, but also mural patterns seen in Islamic art.

Renaissance art incorporated many artistic styles, as it was a period of re-visitation of older styles and works, naturally forming different styles themselves. Medieval, Byzantine and Classical styles were adapted, just to name a few.

If you have more questions, just ask! :D