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

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

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...

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Bibliographic Details
Main Authors: Muhammad Uzair Awan, Artion Kashuri, Kottakkaran Sooppy Nisar, Muhammad Zakria Javed, Sabah Iftikhar, Poom Kumam, Parin Chaipunya
Format: Article
Language:English
Published: SpringerOpen 2022-01-01
Series:Journal of Inequalities and Applications
Subjects:
Trapezium inequality
Harmonic convex function
Riemann–Liouville fractional integrals
Hölder inequality
Power mean inequality
Special means
Online Access:https://doi.org/10.1186/s13660-021-02732-6
Description
Summary: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.
ISSN:1029-242X

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