Trapezoid and Midpoint Type Inequalities for Preinvex Functions via Quantum Calculus

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dc.authoridNtouyas, Sotiris/0000-0002-7695-2118
dc.authoridBudak, Huseyin/0000-0001-8843-955X
dc.authoridTariboon, Jessada/0000-0001-8185-3539
dc.contributor.authorSitho, Surang
dc.contributor.authorAli, Muhammad Aamir
dc.contributor.authorBudak, Huseyin
dc.contributor.authorNtouyas, Sotiris K.
dc.contributor.authorTariboon, Jessada
dc.date.accessioned2021-12-01T18:50:40Z
dc.date.available2021-12-01T18:50:40Z
dc.date.issued2021
dc.department[Belirlenecek]en_US
dc.description.abstractIn this article, we use quantum integrals to derive Hermite-Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We use the q(x)(2)- quantum integral to show midpoint and trapezoidal inequalities for q(x)(2)-differentiable preinvex functions. Furthermore, we demonstrate with an example that the previously proved Hermite- Hadamard-type inequality for preinvex functions via q(x)(1)-quantum integral is not valid for preinvex functions, and we present its proper form. We use q(x)(1)-quantum integrals to show midpoint inequalities for q(x)(1)-differentiable preinvex functions. It is also demonstrated that by considering the limit q -> 1(-) and eta(x(2), x(1)) = -eta(x(1), x(2)) = x(2), x(1) in the newly derived results, the newly proved findings can be turned into certain known results.en_US
dc.description.sponsorshipKing Mongkut's University of Technology North Bangkok [KMUTNB-61-KNOW-030]en_US
dc.description.sponsorshipThis research was funded by King Mongkut's University of Technology North Bangkok, contract No. KMUTNB-61-KNOW-030.en_US
dc.identifier.doi10.3390/math9141666
dc.identifier.issn2227-7390
dc.identifier.issue14en_US
dc.identifier.scopus2-s2.0-85111268366en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.3390/math9141666
dc.identifier.urihttps://hdl.handle.net/20.500.12684/10909
dc.identifier.volume9en_US
dc.identifier.wosWOS:000677330600001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherMdpien_US
dc.relation.ispartofMathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectHermite-Hadamard inequalityen_US
dc.subjectq-integralen_US
dc.subjectquantum calculusen_US
dc.subjectpreinvex functionen_US
dc.subjecttrapezoid inequalitiesen_US
dc.subjectmidpoint inequalitiesen_US
dc.subjectHermite-Hadamard Inequalitiesen_US
dc.subjectIntegral-Inequalitiesen_US
dc.subjectDifferentiable Mappingsen_US
dc.subjectReal Numbersen_US
dc.subjectConvexen_US
dc.titleTrapezoid and Midpoint Type Inequalities for Preinvex Functions via Quantum Calculusen_US
dc.typeArticleen_US

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