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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.

26D15Inequalities for sums, series and integrals of real functions
26A51Convexity, generalizations (one real variable)
Full Text: DOI
[1] Pečarić, J. E.; Proschan, F.; Tong, Y. L.: Convex functions, partial ordering and statistical applications. (1991)
[2] Pearce, C. E. M.; Pecaric, J.: Inequalities for differentiable mappings with application to special means and quadrature formula. Appl. math. Lett. 13, 51-55 (2000) · Zbl 0970.26016
[3] U.S. Kırmacı, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput. (in press)