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Pearce, C. E. M.; Pečarić, J.

Inequalities for differentiable mappings with application to special means and quadrature formulæ. (English) Zbl 0970.26016

Appl. Math. Lett. 13, No. 2, 51-55 (2000).
Summary: Improvements are obtained to some recent error estimates of S. S. Dragomir and R. P. Agarwal [Appl. Math. Lett. 11, No. 5, 91-95 (1998; Zbl 0938.26012)] based on convexity, for the trapezoidal formula. Corresponding estimates are established for the midpoint formula. A parallel development is made based on concavity.

Cited in 1 Review
Cited in 106 Documents

MSC:

26D15 Inequalities for sums, series and integrals
65D30 Numerical integration
26E60 Means

Keywords:

Hermite-Hadamard inequality; integral inequalities; special means; numerical integration; convexity; trapezoidal formula; midpoint formula; concavity

Citations:

Zbl 0938.26012
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Full Text: DOI

References:

[1] Dragomir, S. S.; Agarwal, R. P., Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11, 5, 91-95 (1998) · Zbl 0938.26012
[2] S.S. Dragomir and C.E.M. Pearce, On some inequalities for differentiable convex functions and applications, (preprint).; S.S. Dragomir and C.E.M. Pearce, On some inequalities for differentiable convex functions and applications, (preprint).
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