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A derivative and integral characterization of real-valued convex functions of single variable through the geometric chord property

PE Ezimadu
JN Igabari


Although convex functions have been characterized using the derivative,
integral and monotonicity of the derivative, a characterization which involves a
combination of these concepts has not been achieved. This is the centre of this work. In particular we show that for functions enjoying the geometric chord property, this characterization gives equivalence for the definitions of convexity.

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eISSN: 1116-4336