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On an Iyengar-type inequality involving quadratures in n knots. (English) Zbl 1202.26030
Summary: We give an Iyengar-type inequality involving quadratures in n knots, where n is an arbitrary natural number.
MSC:
26D10Inequalities involving derivatives, differential and integral operators
26D15Inequalities for sums, series and integrals of real functions
References:
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[2]Anastassiou, G. A.; Dragomir, S. S.: On some estimates of the remainder in Taylor’s formula, J. math. Anal. appl. 263, 246-263 (2001) · Zbl 1006.26017 · doi:10.1006/jmaa.2001.7622
[3]Cheng, X. L.: The iyengar type inequality, Appl. math. Lett. 14, 975-978 (2001) · Zbl 0987.26008 · doi:10.1016/S0893-9659(01)00074-X
[4]Elezović, N.; Pečarić, J.: Steffensen’s inequality and estimates of error in trapezoidal rule, Appl. math. Lett. 11, 63-69 (1998) · Zbl 0938.26013 · doi:10.1016/S0893-9659(98)00104-9
[5]Franjić, I.; Pečarić, J.; Perić, I.: Note on an iyengar type inequality, Appl. math. Lett. 19, 657-660 (2006) · Zbl 1136.26005 · doi:10.1016/j.aml.2005.08.018
[6]Iyengar, K. S. K.: Note on an inequality, Math. student 6, 75-76 (1938) · Zbl 64.0209.02