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Home  >  Volume 26 (March 2014)

6. Conditions for the Convexity of a Class of Twice Continuously Differentiable Real-Valued Functions of Several Variables by Peter E. Ezimadu. Volume26, (March, 2014), pp 22 – 27.
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The importance of convex functions in optimization theory calls for the availability of results that ensure their easy recognition. In response to this demand this work presents a characterization which gives an interplay associated with the first order condition, the second order condition, the epigraph, the integral and monotonicity for convex functions. Specifically, it presents a characterization of convex functions by extending an existing result to include the Hessian and epigraph of convex functions; thus providing an equivalence for the definitions of convex functions, and consequently a better horizon for understanding convex functions.