Erratum: Quantum Montgomery identity and quantum estimates of Ostrowski type inequalities

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.

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

Advances in Difference Equations ◽

10.1186/s13662-020-02884-7 ◽

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

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

Journal of Function Spaces ◽

10.1155/2018/6928130 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9 ◽

Cited By ~ 14

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.

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

AIMS Mathematics ◽

10.3934/math.2021114 ◽

2021 ◽

Vol 6 (2) ◽

pp. 1880-1888

Author(s):

Andrea Aglić Aljinović ◽

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Domagoj Kovačević ◽

Mehmet Kunt ◽

Mate Puljiz ◽

...

Keyword(s):

Montgomery Identity

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

Abstract and Applied Analysis ◽

10.1155/2017/5234181 ◽

2017 ◽

Vol 2017 ◽

pp. 1-7 ◽

Cited By ~ 2

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.

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

Symmetry ◽

10.3390/sym12040553 ◽

2020 ◽

Vol 12 (4) ◽

pp. 553 ◽

Cited By ~ 1

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.

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