scholarly journals Correction: Quantum Montgomery identity and quantum estimates of Ostrowski type inequalities

2021 ◽  
Vol 6 (2) ◽  
pp. 1880-1888
Author(s):  
Andrea Aglić Aljinović ◽  
◽  
Domagoj Kovačević ◽  
Mehmet Kunt ◽  
Mate Puljiz ◽  
...  
Keyword(s):  
Montgomery Identity

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 Difference equations related to majorization theorems via Montgomery identity and Green’s functions with application to the Shannon entropy

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Nouman Siddique ◽  
Muhammad Imran ◽  
Khuram Ali Khan ◽  
Josip Pečarić
Keyword(s):  
Shannon Entropy ◽  
Difference Equations ◽  
Green's Functions ◽  
Green’S Functions ◽  
Montgomery Identity

scholarly journals Conformable Fractional Integrals Versions of Hermite-Hadamard Inequalities and Their Generalizations

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Adil Khan ◽  
Yu-Ming Chu ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Gohar Ali
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals ◽  
Montgomery Identity

We prove new Hermite-Hadamard inequalities for conformable fractional integrals by using convex function, s-convex, and coordinate convex functions. We prove new Montgomery identity and by using this identity we obtain generalized Hermite-Hadamard type inequalities.

scholarly journals On Weighted Montgomery Identity for k Points and Its Associates on Time Scales

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Eze R. Nwaeze ◽  
Ana M. Tameru
Keyword(s):  
Weight Function ◽  
Time Scales ◽  
Type Inequality ◽  
Montgomery Identity ◽  
Quantum Calculus ◽  
Ostrowski Type Inequality

The purpose of this paper is to establish a weighted Montgomery identity for k points and then use this identity to prove a new weighted Ostrowski type inequality. Our results boil down to the results of Liu and Ngô if we take the weight function to be the identity map. In addition, we also generalize an inequality of Ostrowski-Grüss type on time scales for k points. For k=2, we recapture a result of Tuna and Daghan. Finally, we apply our results to the continuous, discrete, and quantum calculus to obtain more results in this direction.

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 Extension of Montgomery identity via Taylor polynomial on time scales

2020 ◽  
Vol 44 (5) ◽  
pp. 1708-1723
Author(s):  
Khuram Ali KHAN ◽  
Khalid Mahmood AWAN ◽  
Sumaiya MALIK ◽  
Ammara NOSHEEN
Keyword(s):  
Time Scales ◽  
Taylor Polynomial ◽  
Montgomery Identity

scholarly journals Montgomery Identity and Ostrowski Type Inequalities for a new Quantum Integral

2020 ◽  
Author(s):  
Muhammad Aamir Ali ◽  
H seyin BUDAK ◽  
Mujahid Abbas
Keyword(s):  
Montgomery Identity ◽  
Quantum Integral

scholarly journals A discrete weighted Montgomery identity and Ostrowski type inequalities for functions of two variables

2013 ◽  
Vol 9 (1) ◽  
pp. 47-56
Author(s):  
A. Aglić Aljinović ◽  
J. Pečarić
Keyword(s):  
Montgomery Identity ◽  
Functions Of Two Variables

scholarly journals Generalized Steffensen’s inequality by Montgomery identity

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saad Ihsan Butt ◽  
Asfand Fahad ◽  
Adil Naseer ◽  
Josip Pečarić
Keyword(s):  
Montgomery Identity ◽  
Steffensen’S Inequality

scholarly journals $(\mathrm{p},\mathrm{q})$-Analysis of Montgomery identity and estimates of $(\mathrm{p},\mathrm{q})$-bounds with applications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yu-Ming Chu ◽  
Sadia Talib ◽  
Erhan Set ◽  
Muhammad Uzair Awan ◽  
Muhammad Aslam Noor
Keyword(s):  
Montgomery Identity ◽  
Special Cases ◽  
Quantum Version

AbstractThe main objective of this article is to establish a new post quantum version of Montgomery identity. Some estimates of associated post quantum bounds are also obtained. In order to obtain the main results of the article, we use the preinvexity property of the functions. Some special cases are also discussed in detail. Finally, we present some applications of the obtained results, which shows the significance of the discussed results.

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