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Abstract. Concerning a problem raised by K. Nikodem, we prove the following statement.

Abstract. Characterizations of pairs of stochastic processes that can be separated by Jensen and by affine stochastic processes are presented. As a consequence, some stability results of the Hyers-Ulam-type are obtained.Mathematics Subject Classification. Primary 26A51, Secondary 39B62, 60G99.

Abstract. Based on J. L. W. V. Jensen's concept of convex functions as well on its generalization by E. M. Wright and related to T. Popoviciu's convexity notions, higher-order convexity properties of real functions are introduced and surveyed.Mathematics subject classification (2000): 26A51, 26A48, 39B62.

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