If you are talking about sociology, as I assume you are, then the answer is yes. Functionalism and the functionalist perspective are two different ways of saying the same thing. These are both terms that refer to one of the three major theoretical perspectives in sociology, a perspective that holds that every aspect of society has a specific function that helps maintain stability and order in the society.
To see proof that this is so, let us look at the article in the link below. If you look at the first two sentences under the heading “The Functionalist Perspective,” you will see that the two terms are used interchangeably. The first sentence lists thinkers upon whose works the “functionalist perspective” is based. The second sentence then begins “According to functionalism…” Clearly both sentences are referring to the same thing even though they use two slightly different terms.
“Functionalism” and “the functional perspective,” then, are two terms for the same thing.