TY - JOUR
T1 - Weighted midpoint hermite-hadamard-fejér type inequalities in fractional calculus for harmonically convex functions
AU - Kalsoom, Humaira
AU - Vivas-Cortez, Miguel
AU - Latif, Muhammad Amer
AU - Ahmad, Hijaz
N1 - Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2021/12/2
Y1 - 2021/12/2
N2 - 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.
AB - 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.
KW - Harmonically convex functions
KW - Hermite-Hadamard-Fejér type inequality
KW - Symmetry
KW - Weighted fractional operators
UR - http://www.scopus.com/inward/record.url?scp=85121298449&partnerID=8YFLogxK
U2 - 10.3390/fractalfract5040252
DO - 10.3390/fractalfract5040252
M3 - Article
AN - SCOPUS:85121298449
SN - 2504-3110
VL - 5
JO - Fractal and Fractional
JF - Fractal and Fractional
IS - 4
M1 - 252
ER -