期刊
JOURNAL OF APPROXIMATION THEORY
卷 115, 期 2, 页码 260-288出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1006/jath.2001.3658
关键词
Hermite-Hadamard inequality; two-point quadrature; Lipschitz classes; L-P estimates
类别
We consider a family of two-point quadrature formulae and establish sharp estimates for the remainders under various regularity conditions. Improved forms of certain integral inequalities due to Hermite and Hadamard, Iyengar, Milovanovic and Pecaric, and others are obtained as special cases, Our results can also be interpreted as analogues to a theorem of Ostrowski on the deviation of a function from its averages. Furthermore, we establish a generalization of a result of Fink concerning L-p estimates for the remainder of the trapezoidal rule and present the best constants in the error bounds. (C) 2002 Elsevier Science (USA).
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