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r-convex functions

Mathematical Programming, 1972
A family of real functions, calledr-convex functions, which represents a generalization of the notion of convexity is introduced. This family properly includes the family of convex functions and is included in the family of quasiconvex functions.
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Duality for Closed Convex Functions and Evenly Convex Functions

Journal of Optimization Theory and Applications, 2013
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Volle, M.   +2 more
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CONVEX OPERATOR FUNCTIONS

Mathematics of the USSR-Sbornik, 1972
Let (x) be a convex downwards function, A > 0 a selfadjoint operator in a Hilbert space H, P an orthogonal projector in H; suppose DA PH is dense in PH, and let Ap be the Friedrichs extension of the operator PAP defined on DA PH. The inequality tr (Ap) ≤ tr (PAP) is proved. An estimate for the Jacobi θ-function and a distant generalization of the Szasz
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