Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Nápoles J. E., Guzmán P. M., Bayraktar B. New integral inequalities in the class of functions (h, m)-convex. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 2, pp. 173-183. DOI: 10.18500/1816-9791-2024-24-2-173-183, EDN: WYDLVW

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.05.2024
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English
Heading: 
Mathematics
Article type: 
Article
UDC: 
517.518.86:517.218.244:517.927.2
DOI: 
10.18500/1816-9791-2024-24-2-173-183
EDN: 
WYDLVW

New integral inequalities in the class of functions (h, m)-convex

Автор:
Лачинова Дарья Андреевна
Autors: 
Nápoles Juan E., National University of the Northeast (UNNE)
Guzmán Paulo Matias, National University of the Northeast (UNNE)
Bayraktar Bahtiyar, Bursa Uludag University
Abstract: 

In this article, we have defined new weighted integral operators. We formulated a lemma in which we obtained a generalized identity through these integral operators. Using this identity, we obtain some new generalized Simpson's type inequalities for $(h,m)$-convex functions. These results we obtained using the convexity property, the classical Hölder inequality, and its other form, the power mean inequality. The generality of our results lies in two fundamental points: on the one hand, the integral operator used and, on the other, the notion of convexity. The first, because the ''weight''  allows us to encompass many known integral operators (including the classic Riemann and Riemann – Liouville), and the second, because, under an adequate selection of the parameters, our notion of convexity contains several known notions of convexity. This allows us to show that many of the results reported in the literature are particular cases of ours.

Key words: 
convex functions
(m/h)-convex functions
Simpson’s type inequality
Hermite – Hadamard inequality
Holder inequality
weighted integrals
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Received: 
28.03.2023
Accepted: 
10.10.2023
Published: 
31.05.2024
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