Conformable fractional Newton-type inequalities with respect to differentiable convex functions

The authors propose a new method of investigation of an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established equality. In addition, we prove several N...

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Published inJournal of inequalities and applications Vol. 2023; no. 1; pp. 85 - 19
Main Authors Ünal, Cihan, Hezenci, Fatih, Budak, Hüseyin
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 16.06.2023
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Calculus
Conformable fractional integrals
Convex analysis
Fractional calculus
Inequalities
Integrals
Investigations
Mathematicians
Mathematics
Mathematics and Statistics
Newton formula
Operators (mathematics)
26A51
Conformable fractional integrals
Fractional calculus
26D15
Newton formula
34A08
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Summary:The authors propose a new method of investigation of an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established equality. In addition, we prove several Newton-type inequalities with the aid of Hölder and power-mean inequalities. Furthermore, several new results are given by using special choices of the obtained inequalities. Finally, we give several inequalities of conformable fractional Newton-type for functions of bounded variation.
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/s13660-023-02996-0