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In this paper we show that each strongly λ -convex function f : D → R with modulus c > 0 , where D is an nonempty convex subset of inner product space X with norm ‖·‖ , must by of the form g+ ‖·‖ , where g is an λ -convex function. Moreover, involving the notion of strongly λ -convexity we get a new characterization of inner product space. Mathematics subject classification (2010): Primary 46C15, Secondary 26B25, 39B62.

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