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Abstract. Refinements of Jensen's inequality for operator convex functions, which are generalizations of Mercer's result, are proved. Obtained results are used to refine monotonicity properties for power means of Mercer's type, and a comparision theorem for quasi-arithmetic means of Mercer's type for operators. (2000): 47A63, 47A64. Mathematics subject classification

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Abstract. Two Jensen's type inequalities for convex functions defined on R k which involve elements of convex hulls are given. As their consequences the comparison theorem for weighted L -conjugate means and a Mercer's result are obtained. Mathematics subject classification (2000): 26D15, 26B25.Key words and phrases: Jensen's inequality, convex functions, convex hull. R E F E R E N C E S