Some new parameterized Newton-type inequalities for differentiable functions via fractional integrals

被引：0
作者：
Muhammad Aamir Ali
Christopher S. Goodrich
Hüseyin Budak
机构：
[1] Nanjing Normal University,Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences
[2] UNSW Sydney,School of Mathematics and Statistics
[3] Düzce University,Department of Mathematics, Faculty of Science and Arts
来源：
Journal of Inequalities and Applications | / 2023卷
关键词：
Simpson’s ; formula; Fractional Calculus; Convex Functions; 34A08; 26A51; 26D15;
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摘要：
The main goal of the current study is to establish some new parameterized Newton-type inequalities for differentiable convex functions in the setting of fractional calculus. For this, first we prove a parameterized integral identity involving fractional integrals and then prove Newton-type inequalities for differentiable convex functions. It is also shown that the newly established parameterized inequalities are refinements of the already proved inequalities in the literature for different choices of parameters. Finally, we discuss a mathematical example along with a plot to show the validity of the newly established inequalities.
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