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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:
 26D15 Inequalities for sums, series and integrals of real functions 26A51 Convexity, generalizations (one real variable) 26E60 Means
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##### References:
 [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)