scholarly journals On some Ostrowski type inequalities via Montgomery identity and Taylor's formula

2005 ◽  
Vol 36 (3) ◽  
pp. 199-218 ◽  
Author(s):  
A. Aglic Aljinovic ◽  
J. Pecaric
Keyword(s):  
Integral Means ◽  
Montgomery Identity ◽  
Taylor’S Formula ◽  
The Difference ◽  
Taylor's Formula

A new extension of the weighted Montgomery identity is given, by using Taylor's formula, and used to obtain some Ostrowski type inequalities and the estimations of the difference of two integral means.

scholarly journals On some Ostrowski type inequalities via Montgomery identity and Taylor's formula II

2005 ◽  
Vol 36 (4) ◽  
pp. 279-301 ◽  
Author(s):  
A. Aglic Aljinovic ◽  
J. Pecaric ◽  
A. Vukelic
Keyword(s):  
Integral Means ◽  
Montgomery Identity ◽  
Taylor’S Formula ◽  
The Difference ◽  
Taylor's Formula

A new extension of the weighted Montgomery identity is given, by using Taylor's formula and used to obtain some Ostrowski type inequalities and estimations of the difference of two integral means.

scholarly journals Generalizations of Steffensen’s inequality via the extension of Montgomery identity

2018 ◽  
Vol 16 (1) ◽  
pp. 420-428
Author(s):  
Andrea Aglić Aljinović ◽  
Josip Pečarić ◽  
Anamarija Perušić Pribanić
Keyword(s):  
Convex Functions ◽  
Montgomery Identity ◽  
Taylor’S Formula ◽  
Steffensen’S Inequality ◽  
Grüss Type Inequalities ◽  
Nondecreasing Functions ◽  
New Inequalities ◽  
Taylor's Formula

AbstractIn this paper, we obtained new generalizations of Steffensen’s inequality for n-convex functions by using extension of Montgomery identity via Taylor’s formula. Since 1-convex functions are nondecreasing functions, new inequalities generalize Stefensen’s inequality. Related Ostrowski type inequalities are also provided. Bounds for the reminders in new identities are given by using the Chebyshev and Grüss type inequalities.

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

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.

scholarly journals On Some Estimates of the Remainder in Taylor's Formula

2001 ◽  
Vol 263 (1) ◽  
pp. 246-263 ◽  
Author(s):  
G.A. Anastassiou ◽  
S.S. Dragomir
Keyword(s):  
Taylor’S Formula ◽  
Taylor's Formula

A Derivation of Taylor's Formula with Integral Remainder

2003 ◽  
Vol 76 (3) ◽  
pp. 217
Author(s):  
Dimitri Kountourogiannis ◽  
Paul Loya
Keyword(s):  
Taylor’S Formula ◽  
Taylor's Formula

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

1998 ◽  
Vol 30 (1) ◽  
pp. 133-136 ◽  
Author(s):  
Sui Zhenlin ◽  
Yu Ge ◽  
Yu Zhaoxian
Keyword(s):  
Taylor’S Formula ◽  
Taylor's Formula

q -Taylor's Formula with Its q -Remainder

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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