The Banach contraction principle is the important result, that has many applications. Some authors were interested in this principle in various metric spaces. Branciari A. initiated the notion of the generalized metric space as a generalization of a metric space by replacing the triangle inequality by more general inequality, d(x, y) <= d(x, u) + d(u, v) + d(v, y) for all pairwise distinct points x, y, u, v of X. As such, any metric space is a generalized metric space but the converse is not true. He proved the Banach fixed point theorem in such a space. Some authors proved different types of fixed point theorems by extending the Banach's result. Wardowski D. introduced a new contraction which generalizes the Banach contraction. Using a mapping F : R+ -> R he introduced a new type of contraction called F-contraction and proved a new fixed point theorem concerning F-contraction.