Fixed Point in Semi-linear Uniform Spaces and Convex Metric Spaces

Tallafha, A. and Alhihi S. in [15], asked the following question. If f is a contraction from a complete semi-linear uniform space (X, Γ) to it self, is f has a unique fixed point. In this paper, we shall answer this question negatively and we shall show that convex metric space and Mspace are equivalent except uniqueness. Also, we shall characterize convex metric spaces and use this characterization to give some application using semi-linear uniform spaces.