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    Revista Colombiana de Matemáticas
    Volumen 28 [ 1] ( 1994) Páginas 7-12

    Convex functions and the Hadamard inequality

    Alfonso G Azpeitia
    University of Massachusetts, Boston

    Abstract. The Hadamard inequality is proven without resorting to any properties of the derivative. Only the convexity of the function in a closed interval is needed. Furthermore, if the existence of the integral is assumed, then the convexity requirement is weakened to convexity in the sense of Jensen. Both the Hadamard inequality and a corresponding upper bound are generalized for integrals of the Stieljes type.

    Palabras claves. Convex and concave functions, arithmetic means, convexity inequalities

    Codigo AMS. 1991 26A51.

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