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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2001; 38(6): 1235-1243

Printed November 1, 2001

Copyright © The Korean Mathematical Society.

Hadamard and Dragomir--Agarwal inequalities, higher--order convexity and the Euler formula

Lj. Dedi\'{c}, C. E. M. Pearce, and J. Pe\v{c}ari\'{c}

University of Split, University of Adelaide, University of Adelaide

Abstract

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We obtain bounds relating to Euler’s formula for the case of a function with higher?order convexity properties. These are used to derive estimates of the error involved in the use of the trapezoidal formula for integrating such a function.

Keywords: Hadamard inequality, Euler formula, convex functions, integral inequalities, numerical integration

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