A New Inclusion on Inequalities of the Hermite–Hadamard–Mercer Type for Three-Times Differentiable Functions

Autor:	Talib Hussain, Loredana Ciurdariu, Eugenia Grecu
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	generalized fractional integrals Hermite–Hadamard inequality Jensen–Mercer inequality Hermite–Hadamard–Mercer inequality Hölder’s inequality power mean inequality Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 23, p 3711 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12233711
Popis:	The goal of this study is to develop numerous Hermite–Hadamard–Mercer (H–H–M)-type inequalities involving various fractional integral operators, including classical, Riemann–Liouville (R.L), k-Riemann–Liouville (k-R.L), and their generalized fractional integral operators. In addition, we establish a number of corresponding fractional integral inequalities for three-times differentiable convex functions that are connected to the right side of the H–H–M-type inequality. For these results, further remarks and observations are provided. Following that, a couple of graphical representations are shown to highlight the key findings of our study. Finally, some applications on special means are shown to demonstrate the effectiveness of our inequalities.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/187e24efeed9444a9297e4ce3f80e4f0 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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