Converse Ohlin’s lemma for convex and strongly convex functions. (English) Zbl 1519.26004
In this paper, the authors derive and prove the converse of Ohlin’s result for convex and strongly comvex functions. Furthermore, they use the new results to give new proofs of the well-known probabilistic characterizations of convex and strongly convex functions.
Reviewer: James Adedayo Oguntuase (Abeokuta)
MSC:
| 26A51 | Convexity of real functions in one variable, generalizations |
| 26D15 | Inequalities for sums, series and integrals |
| 39B62 | Functional inequalities, including subadditivity, convexity, etc. |
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