Strongly λ -convex functions and some characterization of inner product spaces

摘要

In this paper we show that each strongly λ -convex function f : D → R with modulus c 0,whereD is an nonempty convex subset of inner product space X with norm · ,must by of the form g + · 2 ,where g is an λ -convex function. Moreover, involving the notion of strongly λ -convexity we get a new characterization of inner product space.