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

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.

scholarly journals Some New q—Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex Functions

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 553 ◽  
Author(s):  
Miguel Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández Hernández
Keyword(s):  
Integral Inequalities ◽  
Montgomery Identity ◽  
Quantum Calculus ◽  
Special Cases ◽  
Preinvex Functions

In this work the authors establish a new generalized version of Montgomery’s identity in the setting of quantum calculus. From this result, some new estimates of Ostrowski type inequalities are given using preinvex functions. Given the generality of preinvex functions, particular q —integral inequalities are established with appropriate choice of the parametric bifunction. Some new special cases from the main results are obtained and some known results are recaptured as well. At the end, a briefly conclusion is given.

scholarly journals Montgomery identity and Ostrowski-type inequalities via quantum calculus

2021 ◽  
Vol 19 (1) ◽  
pp. 1098-1109
Author(s):  
Thanin Sitthiwirattham ◽  
Muhammad Aamir Ali ◽  
Huseyin Budak ◽  
Mujahid Abbas ◽  
Saowaluck Chasreechai
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Montgomery Identity ◽  
Quantum Calculus ◽  
Special Cases ◽  
Quantum Version

Abstract In this paper, we prove a quantum version of Montgomery identity and prove some new Ostrowski-type inequalities for convex functions in the setting of quantum calculus. Moreover, we discuss several special cases of newly established inequalities and obtain different new and existing inequalities in the field of integral inequalities.

scholarly journals Hermite–Hadamard–Fejér-Type Inequalities and Weighted Three-Point Quadrature Formulae

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1720
Author(s):  
Mihaela Ribičić Penava
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Formula ◽  
Higher Order ◽  
Quadrature Formulae ◽  
Special Cases

The goal of this paper is to derive Hermite–Hadamard–Fejér-type inequalities for higher-order convex functions and a general three-point integral formula involving harmonic sequences of polynomials and w-harmonic sequences of functions. In special cases, Hermite–Hadamard–Fejér-type estimates are derived for various classical quadrature formulae such as the Gauss–Legendre three-point quadrature formula and the Gauss–Chebyshev three-point quadrature formula of the first and of the second kind.

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 Improvement in companion of Ostrowski type inequalities for mappings whose first derivatives are of bounded variation and applications

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5305-5314 ◽  
Author(s):  
Hüseyin Budaka ◽  
Mehmet Sarikaya ◽  
Ather Qayyum
Keyword(s):  
Bounded Variation ◽  
Integral Inequalities ◽  
Quadrature Formulae ◽  
Special Cases ◽  
Type Integral

The main aim of this paper is to obtain a improved and generalized version of companion of Ostrowski type integral inequalities for mappings whose first derivatives are of bounded variation. Some previous results are also recaptured as special cases. New quadrature formulae are also provided.

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 Some new generalized $ \kappa $–fractional Hermite–Hadamard–Mercer type integral inequalities and their applications

2021 ◽  
Vol 7 (2) ◽  
pp. 3203-3220
Author(s):  
Miguel Vivas-Cortez ◽  
◽  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Artion Kashuri ◽  
...  
Keyword(s):  
Quadrature Formula ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Error Estimations ◽  
Integral Identities

<abstract><p>In this paper, we have established some new Hermite–Hadamard–Mercer type of inequalities by using $ {\kappa} $–Riemann–Liouville fractional integrals. Moreover, we have derived two new integral identities as auxiliary results. From the applied identities as auxiliary results, we have obtained some new variants of Hermite–Hadamard–Mercer type via $ {\kappa} $–Riemann–Liouville fractional integrals. Several special cases are deduced in detail and some know results are recaptured as well. In order to illustrate the efficiency of our main results, some applications regarding special means of positive real numbers and error estimations for the trapezoidal quadrature formula are provided as well.</p></abstract>

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.

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