SHARP INTEGRAL INEQUALITIES BASED ON GENERAL TWO-POINT FORMULAE VIA AN EXTENSION OF MONTGOMERY’S IDENTITY

The ANZIAM Journal ◽

10.1017/s1446181109000315 ◽

2009 ◽

Vol 51 (1) ◽

pp. 67-101 ◽

Author(s):

A. AGLIĆ ALJINOVIĆ ◽

J. PEČARIĆ ◽

M. RIBIČIĆ PENAVA

Keyword(s):

Integral Inequalities ◽

Quadrature Formulae ◽

Taylor’S Formula ◽

Taylor's Formula

AbstractWe consider families of general two-point quadrature formulae, using the extension of Montgomery’s identity via Taylor’s formula. The formulae obtained are used to present a number of inequalities for functions whose derivatives are fromLpspaces and Bullen-type inequalities.

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Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery Identity

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2012/343191 ◽

2012 ◽

Vol 2012 ◽

pp. 1-12

Author(s):

J. Pečarić ◽

M. Ribičić Penava

Keyword(s):

Quadrature Formula ◽

Integral Inequalities ◽

Montgomery Identity ◽

Quadrature Formulae ◽

Taylor’S Formula ◽

Special Cases ◽

Taylor's Formula

We consider families of general four-point quadrature formulae using a generalization of the Montgomery identity via Taylor’s formula. The results are applied to obtain some sharp inequalities for functions whose derivatives belong to spaces. Generalizations of Simpson’s 3/8 formula and the Lobatto four-point formula with related inequalities are considered as special cases.

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Taylor’s Formula and Integral Inequalities for Conformable Fractional Derivatives

Contributions in Mathematics and Engineering ◽

10.1007/978-3-319-31317-7_2 ◽

2016 ◽

pp. 25-43 ◽

Author(s):

Douglas R. Anderson

Keyword(s):

Fractional Derivatives ◽

Integral Inequalities ◽

Taylor’S Formula ◽

Taylor's Formula

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On Some Estimates of the Remainder in Taylor's Formula

Journal of Mathematical Analysis and Applications ◽

10.1006/jmaa.2001.7622 ◽

2001 ◽

Vol 263 (1) ◽

pp. 246-263 ◽

Author(s):

G.A. Anastassiou ◽

S.S. Dragomir

Keyword(s):

Taylor’S Formula ◽

Taylor's Formula

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A Derivation of Taylor's Formula with Integral Remainder

Mathematics Magazine ◽

10.2307/3219325 ◽

2003 ◽

Vol 76 (3) ◽

pp. 217

Author(s):

Dimitri Kountourogiannis ◽

Paul Loya

Keyword(s):

Taylor’S Formula ◽

Taylor's Formula

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On Taylor’s formula for the resolvent of a complex matrix

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2008.03.051 ◽

2008 ◽

Vol 56 (9) ◽

pp. 2285-2288 ◽

Author(s):

Matthew X. He ◽

Paolo E. Ricci

Keyword(s):

Complex Matrix ◽

Taylor’S Formula ◽

Taylor's Formula

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q, s -Taylor's Formula with q, s -Remainder

Communications in Theoretical Physics ◽

10.1088/0253-6102/30/1/133 ◽

1998 ◽

Vol 30 (1) ◽

pp. 133-136 ◽

Author(s):

Sui Zhenlin ◽

Yu Ge ◽

Yu Zhaoxian

Keyword(s):

Taylor’S Formula ◽

Taylor's Formula

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q -Taylor's Formula with Its q -Remainder

Communications in Theoretical Physics ◽

10.1088/0253-6102/23/1/117 ◽

1995 ◽

Vol 23 (1) ◽

pp. 117-120 ◽

Author(s):

Si-Cong Jing ◽

Hong-Yi Fan

Keyword(s):

Taylor’S Formula ◽

Taylor's Formula

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q-Taylor’s Formula for Polynomials

Quantum Calculus - Universitext ◽

10.1007/978-1-4613-0071-7_4 ◽

2002 ◽

pp. 12-13

Author(s):

Victor Kac ◽

Pokman Cheung

Keyword(s):

Taylor’S Formula ◽

Taylor's Formula

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Generalized Taylor’s Formula for Polynomials

Quantum Calculus - Universitext ◽

10.1007/978-1-4613-0071-7_2 ◽

2002 ◽

pp. 5-6

Author(s):

Victor Kac ◽

Pokman Cheung

Keyword(s):

Taylor’S Formula ◽

Generalized Taylor’S Formula ◽

Taylor's Formula

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A Partition of Unity and Taylor's Formula

Series on Analysis, Applications and Computation - An Introduction to Pseudo-Differential Operators ◽

10.1142/9789814583091_0007 ◽

2014 ◽

pp. 43-53

Keyword(s):

Partition Of Unity ◽

Taylor’S Formula ◽

Taylor's Formula

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