Uniform convexity, strong convexity and property UC.

Property UC, introduced in 2009, plays a crucial role in several existence and convergence results for best proximity points and fixed points. In this paper, we present two approximation theoretic characterizations of uniform convexity and as consequences of these results, we characterize the uniform convexity in terms of property UC. Characterizations of strong convexity in terms of property UC are also presented. [ABSTRACT FROM AUTHOR]