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Jensen’s and Hermite-Hadamard’s type inequalities for lower and strongly convex functions on normed spaces. (English) Zbl 1409.26005

Summary: In this paper, we obtain some Jensen’s and Hermite-Hadamard’s type inequalities for lower, upper, and strongly convex functions defined on convex subsets in normed linear spaces. The case of inner product space is of interest since in these case the concepts of lower convexity and strong convexity coincides. Applications for univariate functions of real variable and the connections with earlier Hermite-Hadamard’s type inequalities are also provided.

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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