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Nonstability results in the theory of convex functions. (English) Zbl 1108.39028
Summary: We show that the inequality defining convex functions (convex in the sense of Wright) is not stable in infinitely-dimensional spaces. The inequality defining Jensen-convex functions is not stable either, even if its domain is a real interval.
MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B62 Functional inequalities, including subadditivity, convexity, etc.
26A51 Convexity of real functions in one variable, generalizations
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