Strictly convex normed linear spaces

A new characterization of strict convexity for complex normed linear spaces in terms of duality maps is given. It is then shown that many of the latest characterizations of strict convexity follow as simple corollaries. In this paper we give another characterization of s.c. normed linear spaces in terms of duality maps. This result can be used to unify and prove many of the other latest characterizations. For example, as simple corollaries of our result we obtain a characterization due to Menaker (15) (and mentioned by Palmer (16)), a characterization stated (but not proved) by Berkson (1), a characterization due to Torrance (20), a characterization half of which was proved by Husain and Malviya (10) and finally, a generalization of Petryshyn's characterization (7), (17), (19) to complex spaces.