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In this paper we define the so-called (k; h)-convex function which is a natural generalization of the usual convexity, the s-convexity in the first and second sense, the h-convexity, the Godunova-Levin functions and the P-functions. Some regularity and Bernstein-Doetsch type results are investigated for (k; h)-convex functions.

Bernstein-Doetsch type results for $(k, h)$-convex functions