Weighted Midpoint Hermite-Hadamard-Fejér Type Inequalities in Fractional Calculus for Harmonically Convex Functions

Fractal and Fractional

Muhammad Amer Latif¹  Humaira Kalsoom²  Miguel Vivas-Cortez³  Hijaz Ahmad⁴ 

[1] Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Hofuf 31982, Saudi Arabia;Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;Escuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Naturales y Exactas Pontificia, Universidad Católica del Ecuador, Sede Quito 17-01-2184, Ecuador;Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy;

关键词: symmetry;    weighted fractional operators;    harmonically convex functions;    Hermite-Hadamard-Fejér type inequality;   

DOI  :  10.3390/fractalfract5040252

来源: DOAJ

【 摘 要 】

In this paper, we establish a new version of Hermite-Hadamard-Fejér type inequality for harmonically convex functions in the form of weighted fractional integral. Secondly, an integral identity and some weighted midpoint fractional Hermite-Hadamard-Fejér type integral inequalities for harmonically convex functions by involving a positive weighted symmetric functions have been obtained. As shown, all of the resulting inequalities generalize several well-known inequalities, including classical and Riemann–Liouville fractional integral inequalities.

【 授权许可】

Unknown