Integral inequalities for s -convex functions via generalized conformable fractional integral operators

Advances in Difference Equations

article

Kashuri, Artion¹  Iqbal, Sajid²  Liko, Rozana¹  Gao, Wei³  Samraiz, Muhammad⁴ 

[1] Department of Mathematics, Faculty of Technical Science, University Ismail Qemali;Department of Mathematics, University of Management and Technology;School of Information Science and Technology, Yunnan Normal University;Department of Mathematics, University of Sargodha

关键词: Hermite–Hadamard inequality;    Hölder inequality;    Power mean inequality;    Convexity;    Conformable fractional integral;    General fractional integral operators;   

DOI  :  10.1186/s13662-020-02671-4

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We introduce new operators, the so-called left and right generalized conformable fractional integral operators. By using these operators we establish new Hermite–Hadamard inequalities for s-convex functions and products of two s-convex functions in the second sense. Also, we obtain two interesting identities for a differentiable function involving a generalized conformable fractional integral operator. By applying these identities we give Hermite–Hadamard and midpoint-type integral inequalities for s-convex functions. Different special cases have been identified and some known results are recovered from our general results. These results may motivate further research in different areas of pure and applied sciences.

【 授权许可】

CC BY