New Form of Newton-Type Inequalities for Multiplicative Conformable Fractional Integrals

In this study, a new Newton-type inequality form for multiplicative convex functions is derived using multiplicative conformable fractional integrals. The developed new form presents an inequality that has not been encountered before in literature. To obtain the main results, an essential identity i...

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Published inJournal of mathematical sciences and modelling Vol. 8; no. 2; pp. 93 - 111
Main Authors Budak, Hüseyin, Ergün, Büşra Betül
Format Journal Article
LanguageEnglish
Published Mahmut Akyigit 28.06.2025
Subjects
conformable fractional integrals
convex functions
multiplicative calculus
newton inequality
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Abstract In this study, a new Newton-type inequality form for multiplicative convex functions is derived using multiplicative conformable fractional integrals. The developed new form presents an inequality that has not been encountered before in literature. To obtain the main results, an essential identity is first introduced, and this identity is combined with multiplicative conformable fractional integrals to create a new Newton-type inequality. This work not only provides a significant contribution to previous research on multiplicative convex functions but also offers a new perspective on the subject. Future research may aim to explore the application of this form to different fractional integral operators or function types.
AbstractList In this study, a new Newton-type inequality form for multiplicative convex functions is derived using multiplicative conformable fractional integrals. The developed new form presents an inequality that has not been encountered before in literature. To obtain the main results, an essential identity is first introduced, and this identity is combined with multiplicative conformable fractional integrals to create a new Newton-type inequality. This work not only provides a significant contribution to previous research on multiplicative convex functions but also offers a new perspective on the subject. Future research may aim to explore the application of this form to different fractional integral operators or function types.
Author Budak, Hüseyin
Ergün, Büşra Betül
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Snippet In this study, a new Newton-type inequality form for multiplicative convex functions is derived using multiplicative conformable fractional integrals. The...
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StartPage 93
SubjectTerms conformable fractional integrals
convex functions
multiplicative calculus
newton inequality
Title New Form of Newton-Type Inequalities for Multiplicative Conformable Fractional Integrals
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