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Problemy Analiza — Issues of Analysis, 2024, Volume 13(31), Issue 2, Pages 106–127
DOI: https://doi.org/10.15393/j3.art.2024.15450 (Mi pa401) 		 
Milne-type integral inequalities for modified $(h,m)$-convex functions on fractal sets

J. E. Nápolesab, P. M. Guzmánac, B. Bayraktard

a UNNE, FaCENA, Ave. Libertad 5450, Corrientes 3400, Argentina
b UTN-FRRE, French 414, Resistencia, Chaco 3500, Argentina
c UNNE, Facultad de Ciencias Agrarias Sargento Cabral 2131, Corrientes, Argentina
d Bursa Uludag University, Faculty of Education, Gorukle Campus, 16059, Bursa, Turkey.
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DOI: https://doi.org/10.15393/j3.art.2024.15450
Abstract: In the article, new versions of integral inequalities of Milne type are derived for $(h, m)$-convex modified functions of the second type on fractal sets. Based on a new generalized local fractional weighted integral operator, an identity is established as the foundation for subsequently obtained inequalities. Throughout our study, we obtained certain results known in the literature, which include particular cases of our findings.
Keywords: local fractional derivatives, local fractional integrals, fractal sets, Milne inequality, $(h,m)$-convex modified functions of second type, Hölder inequality, power mean inequality.
Received: 28.12.2023
Revised: 25.03.2024
Accepted: 26.03.2024
Document Type: Article
UDC: 517.518.862, 517.218.244
MSC: Primary 26A33; Secondary 26D10, 47A63
Language: English
Citation: J. E. Nápoles, P. M. Guzmán, B. Bayraktar, “Milne-type integral inequalities for modified $(h,m)$-convex functions on fractal sets”, Probl. Anal. Issues Anal., 13(31):2 (2024), 106–127
Citation in format AMSBIB
\Bibitem{NapGuzBay24}
\by J.~E.~N\'apoles, P.~M.~Guzm\'an, B.~Bayraktar
\paper Milne-type integral inequalities for modified $(h,m)$-convex functions on fractal sets
\jour Probl. Anal. Issues Anal.
\yr 2024
\vol 13(31)
\issue 2
\pages 106--127
\mathnet{http://mi.mathnet.ru/pa401}
\crossref{https://doi.org/10.15393/j3.art.2024.15450}
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