New conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in terms of generalized conformable fractional operators via majorization

• Autorzy: Saeed Tareq , Khan Muhammad Adil , Faisal Shah , Alsulami Hamed H. , Alhodaly Mohammed Sh.

Identyfikatory

DOI

10.1515/dema-2022-0225

• Języki publikacji: EN

Abstrakty

EN

The Hermite-Hadamard inequality is regarded as one of the most favorable inequalities from the research point of view. Currently, mathematicians are working on extending, improving, and generalizing this inequality. This article presents conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in weighted and unweighted forms by using the idea of majorization and convexity together with generalized conformable fractional integral operators. They not only represent continuous and discrete inequalities in compact form but also produce generalized inequalities connecting various fractional operators such as Hadamard, Katugampola, Riemann-Liouville, conformable, and Rieman integrals into one single form. Also, two new integral identities have been investigated pertaining a differentiable function and three tuples. By using these identities and assuming ∣f'∣ and ∣f'∣q(q>1) as convex, we deduce bounds concerning the discrepancy of the terms of the main inequalities.

Słowa kluczowe

EN

Jensen's inequality; Mercer inequality; Hermite-Hadamard inequality; Hölder inequality; majorization theory

PL

nierówności Jensena; nierówność Mercera; nierówność typu Hermite'a-Hadamarda; nierówność Höldera; majoryzacja

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220225
• Opis fizyczny: Bibliogr. 51 poz.

Twórcy

autor

Saeed Tareq

• Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

autor

Khan Muhammad Adil

• Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

autor

Faisal Shah

• Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

autor

Alsulami Hamed H.

• Financial Mathematics and Actuarial Science (FMAS) – Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

autor

Alhodaly Mohammed Sh.

• Financial Mathematics and Actuarial Science (FMAS) – Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).