Some k-fractional extensions of the trapezium inequalities through generalized relative semi-(m,h)-preinvexity

In this paper, we first introduce the concept of generalized relative semi- -preinvex functions, and then a new k-Riemann-Liouville fractional integral identity for differentiable mapping is derived. With the help of this identity, we present some new bounds on trapezium inequalities via generalized...

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Bibliographic Details
Published inApplicable analysis Vol. 100; no. 3; pp. 642 - 662
Main Authors Du, Tingsong, Awan, Muhammad Uzair, Kashuri, Artion, Zhao, Shasha
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 17.02.2021
Taylor & Francis Ltd
Subjects
G. M. N'Guerekata
generalized relative semi
Inequalities
k-Riemann-Liouville fractional integrals
preinvex functions
Primary 26A33
Secondary 26D15
Trapezium inequality
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ISSN0003-6811
1563-504X
DOI10.1080/00036811.2019.1616083

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Summary:In this paper, we first introduce the concept of generalized relative semi- -preinvex functions, and then a new k-Riemann-Liouville fractional integral identity for differentiable mapping is derived. With the help of this identity, we present some new bounds on trapezium inequalities via generalized relative semi- -preinvexity. It is pointed out that some new and known special cases can be deduced from main results of the article.
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2019.1616083