On some new inequalities of Hermite-Hadamard type for functions whose derivatives are \(s\)-convex in the second sense in the absolute value. (English. Ukrainian original) Zbl 1386.26030
Ukr. Math. J. 67, No. 10, 1552-1571 (2016); translation from Ukr. Mat. Zh. 67, No. 10, 1380-1397 (2015).
Summary: Several new inequalities of the Hermite-Hadamard type are established for functions whose derivatives are \(s\)-convex in the second sense in the absolute value. Some applications to special means of positive real numbers are also presented.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26A51 | Convexity of real functions in one variable, generalizations |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 65D30 | Numerical integration |
| 26E60 | Means |
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