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

Journal of Inequalities and Applications

Research

Fatih Hezenci¹  Hüseyin Budak¹  Cihan Ünal² 

[1] Department of Mathematics, Faculty of Science and Arts, Duzce University, 81620, Duzce, Turkey;Department of Mathematics, Faculty of Science and Arts, Sinop University, 57000, Sinop, Turkey;

关键词: Newton formula;    Fractional calculus;    Conformable fractional integrals;    26A51;    26D15;    34A08;   

DOI  :  10.1186/s13660-023-02996-0

 received in 2023-03-23, accepted in 2023-06-08,  发布年份 2023

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY   
© The Author(s) 2023

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