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On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula. (English) Zbl 1043.26012
Summary: Some inequalities are presented here for differentiable convex mappings, using Hermite-Hadamard’s integral inequality holding for convex functions. A parallel development is deduced for differentiable concave functions. Some applications to special means of real numbers are also given. Finally, some error estimates for the midpoint formula are obtained.
MSC:
26D15Inequalities for sums, series and integrals of real functions
26A51Convexity, generalizations (one real variable)
26E60Means