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

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 inequalit...

Full description

Saved in:
Bibliographic Details
Published inJournal of inequalities and applications Vol. 2023; no. 1; pp. 49 - 17
Main Authors Ali, Muhammad Aamir, Goodrich, Christopher S., Budak, Hüseyin
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 04.04.2023
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Approximation
Calculus
Convex analysis
Convex Functions
Fractional Calculus
Inequalities
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Parameterization
Simpson’s 3 8 $\frac{3}{8}$ formula
Fractional Calculus
26A51
formula
Convex Functions
Simpson’s
26D15
34A08
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-023-02953-x