Convexity of Chebyshev Sets Through Differentiability of Distance   Function
  In this paper, we study a part of approximation theory that presents the conditions under which a \Ceby\sev set in a Banach space is convex. To do so, we use Gateaux differentiability of the distance function. 
A. Assadi, H. Haghshenas and H. Hosseini Guive