Certain mean-type fractional integral inequalities via different convexities with applications

Journal of inequalities and applications

article

Muhammad Samraiz¹  Fakhra Nawaz¹  Sajid Iqbal²  Thabet Abdeljawad³  Gauhar Rahman⁶  Kottakkaran Sooppy Nisar⁷ 

[1] Department of Mathematics, University of Sargodha;Department of Mathematics, University of Management and Technology;Department of Mathematics and General Sciences, Prince Sultan University;Department of Medical Research, China Medical University;Department of Computer Science and Information Engineering, Asia University;Department of Mathematics, Shaheed Benazir Bhutto University;Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University

关键词: Mean-type inequalities;    h -convex;    \((s+1)\) -convex;    k -conformable integral;    \((k;    s)\) -Riemann–Liouville fractional integral;    Conformable integral;    Trapezoid inequalities;   

DOI  :  10.1186/s13660-020-02474-x

学科分类：电力

来源: SpringerOpen

【 摘 要 】

In this paper, we establish certain generalized fractional integral inequalities of mean and trapezoid type for $(s+1)$ -convex functions involving the $(k,s)$ -Riemann–Liouville integrals. Moreover, we develop such integral inequalities for h-convex functions involving the k-conformable fractional integrals. The legitimacy of the derived results is demonstrated by plotting graphs. As applications of the derived inequalities, we obtain the classical Hermite–Hadamard and trapezoid inequalities.

【 授权许可】

CC BY