New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas

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Publication Details

Author list: Awan M.U., Kashuri A., Nisar K.S., Javed M.Z., Iftikhar S., Kumam P., Chaipunya P.

Publisher: SpringerOpen

Publication year: 2022

Journal: Journal of Inequalities and Applications (1025-5834)

Volume number: 2022

Issue number: 1

ISSN: 1025-5834

eISSN: 1029-242X

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85122203585&doi=10.1186%2fs13660-021-02732-6&partnerID=40&md5=294c763ff4b8bb3a4e9fe4558d86d553

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained. © 2021, The Author(s).

Keywords

Error estimations, Harmonic convex function, Hölder inequality, Power mean inequality, Riemann–Liouville fractional integrals, Trapezium inequality