Fractional Hermite-Hadamard inequality and error estimates for Simpson's formula through convexity with respect to a pair of functions

In this article, we establish two new and different versions of fractional Hermite-Hadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new Simpson's type inequalities for differentiable convex functions with respect to a pair of functi...

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Bibliographic Details
Published in:Mathematical notes (Miskolci Egyetem (Hungary)) Vol. 24; no. 2; pp. 553 - 568
Main Authors: Ali, Muhammad Aamir, Soontharanon, Jarunee, Budak, Hüseyin, Sitthiwirattham, Thanin, Fečkan, Michal
Format: Journal Article
Language:English
Published: Miskolc University of Miskolc 2023
Subjects:
Calculus
Convex analysis
Convexity
Estimates
Inequalities
Integrals
R&D
Research & development
ISSN:1787-2405, 1787-2413
Online Access:Get full text
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Summary:In this article, we establish two new and different versions of fractional Hermite-Hadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new Simpson's type inequalities for differentiable convex functions with respect to a pair of functions. We also prove two more Simpson's type inequalities for differentiable convex functions with respect to a pair of functions using the power mean and Holder's inequalities. It is also shown that the newly established inequalities are the extension of some existing results. Finally, we add some mathematical examples and their graphs to show the validity of newly established results.
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ISSN:1787-2405
1787-2413
DOI:10.18514/MMN.2023.4214