Levinson-type inequalities via new Green functions and Montgomery identity-Reference-Cited by-同舟云学术

Levinson-type inequalities via new Green functions and Montgomery identity

Published:2020-01-01 Issue:1 Volume:18 Page:632-652
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Adeel Muhammad¹²,Khan Khuram Ali¹²,Pečarić Ðilda³,Pečarić Josip⁴

Affiliation:

1. Department of Mathematics, University of Sargodha , Sargodha-40100 , Pakistan

2. Department of Mathematics, University of Central Punjab , Lahore , Pakistan

3. Catholic University of Croatia , Ilica 242 , Zagreb , Croatia

4. Rudn University , Moscow , Russia

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0163/pdf

Reference32 articles.

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3. D. S. Mitrinović, J. Pečarić, and A. M. Fink, Classical and New Inequalities in Analysis, vol. 61, Kluwer Academic Publishers, Dordrecht, 1991.

4. T. Popoviciu, Sur une inegalite de N. Levinson. Mathematica 6 (1969), 301–306.

5. P. S. Bullen, An inequality of N. Levinson, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 412/460 (1973), 109–112.

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