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 Generalizations of Steffensen’s inequality via Taylor’s formula

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Josip Pečarić ◽  
Anamarija Perušić Pribanić ◽  
Ksenija Smoljak Kalamir
Keyword(s):  
Taylor’S Formula ◽  
Steffensen’S Inequality ◽  
Taylor's Formula

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 Generalizations of Steffensen’s inequality via two-point Abel-Gontscharoff polynomial

2019 ◽  
Vol 27 (2) ◽  
pp. 121-137
Author(s):  
Josip Pečarić ◽  
Anamarija Perušić Pribanić ◽  
Ksenija Smoljak Kalamir
Keyword(s):  
Convex Functions ◽  
Steffensen’S Inequality ◽  
Čebyšev Functional ◽  
Grüss Type Inequalities

Abstract Using two-point Abel-Gontscharoff interpolating polynomial some new generalizations of Steffensen’s inequality for n−convex functions are obtained and some Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using the Čebyšev functional some new bounds for the remainder in obtained generalizations are proven and related Grüss-type inequalities are given.

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 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 Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
Definition Of ◽  
The Given ◽  
Class Of Functions ◽  
Interval Valued ◽  
New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

scholarly journals Levinson-type inequalities via new Green functions and Montgomery identity

2020 ◽  
Vol 18 (1) ◽  
pp. 632-652 ◽  
Author(s):  
Muhammad Adeel ◽  
Khuram Ali Khan ◽  
Ðilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Convex Functions ◽  
Green Functions ◽  
Montgomery Identity ◽  
Data Points

Abstract In this study, Levinson-type inequalities are generalized by using new Green functions and Montgomery identity for the class of k-convex functions (k ≥ 3). Čebyšev-, Grüss- and Ostrowski-type new bounds are found for the functionals involving data points of two types. Moreover, a new functional is introduced based on {\mathfrak{f}} divergence and then some estimates for new functional are obtained. Some inequalities for Shannon entropies are obtained too.

scholarly journals Post-quantum Hermite–Hadamard type inequalities for interval-valued convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Ghulam Murtaza ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Fundamental Properties ◽  
Interval Valued ◽  
New Inequalities

AbstractIn this research, we introduce the notions of $(p,q)$ ( p , q ) -derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities of Hermite–Hadamard type for interval-valued convex functions employing the newly defined integral and derivative. Moreover, we find the estimates for the newly proved inequalities of Hermite–Hadamard type. It is also shown that the results proved in this study are the generalization of some already proved research in the field of Hermite–Hadamard inequalities.

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
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