Strong convexity and separation theorems. (English) Zbl 1342.26029
The characterizations of a pair of functions that can be separated by a strongly convex, approximately concave or c-quadratic-affine functions are presented, proved and discussed. Connections of the results obtained to some earlier results in this area in the literature are well pointed out. Furthermore, stability results of the Hyers-Ulam type are derived as consequences of the results obtained.
Reviewer: James Adedayo Oguntuase (Abeokuta)
MSC:
| 26A51 | Convexity of real functions in one variable, generalizations |
| 39B62 | Functional inequalities, including subadditivity, convexity, etc. |
Keywords:
strongly convex functions; approximately concave functions; \(c\)-quadratic-affine functions; separation theorems; Hyers-Ulam stabilityReferences:
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