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Year
2021
Volume
31
Issue
4
Pages
597-612
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Section Mathematics
Title New Hadamard-type inequalities via $(s,m_{1},m_{2})$-convex functions
Author(-s) Bayraktar B.a, Butt S.I.b, Shaokat Sh.b, Napoles Valdes J.E.cd
Affiliations Bursa Uludag Universitya, COMSATS University Islamabadb, Universidad Nacional del Nordestec, Universidad Tecnologica Nacionald
Abstract The article introduces a new concept of convexity of a function: $(s,m_{1},m_{2})$-convex functions. This class of functions combines a number of convexity types found in the literature. Some properties of $(s,m_{1},m_{2})$-convexities are established and simple examples of functions belonging to this class are given. On the basis of the proved identity, new integral inequalities of the Hadamard type are obtained in terms of the fractional integral operator. It is shown that these results give us, in particular, generalizations of a number of results available in the literature.
Keywords convex function, Hadamard type inequality, Riemann–Liouville fractional integral, Hölder inequality, power mean inequality
UDC 517.518, 517.218, 517.928
MSC 26A33, 26A51, 26D15
DOI 10.35634/vm210405
Received 14 July 2021
Language English
Citation Bayraktar B., Butt S.I., Shaokat Sh., Napoles Valdes J.E. New Hadamard-type inequalities via $(s,m_{1},m_{2})$-convex functions, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 4, pp. 597-612.
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