A comprehensive review of the Hermite–Hadamard inequality pertaining to fractional integral operators

M Tariq, SK Ntouyas, AA Shaikh - Mathematics, 2023 - mdpi.com
In the frame of fractional calculus, the term convexity is primarily utilized to address several
challenges in both pure and applied research. The main focus and objective of this review …

Integral inequalities via Raina's fractional integrals operator with respect to a monotone function

SB Chen, S Rashid, Z Hammouch, MA Noor… - Advances in Difference …, 2020 - Springer
We establish certain new fractional integral inequalities involving the Raina function for
monotonicity of functions that are used with some traditional and forthright inequalities …

[PDF][PDF] Study of inequalities for unified integral operators of generalized convex functions

G Farid, K Mahreen, YM Chu - Open Journal of Mathematical Sciences, 2021 - pisrt.org
The aim of this paper is to study unified integral operators for generalized convex functions
namely (α, h− m)-convex functions. We obtained upper as well as lower bounds of these …

Inequalities for Unified Integral Operators via Strongly (α, hm)‐Convexity

Z Zhang, G Farid, K Mahreen - Journal of Function Spaces, 2021 - Wiley Online Library
In this paper, we give a generalized definition namely strongly (α, h‐m)‐convex function that
unifies many known definitions. By applying this new definition, we present inequalities for …

On boundedness of unified integral operators for quasiconvex functions

D Zhao, G Farid, M Zeb, S Ahmad… - Advances in Difference …, 2020 - Springer
This work deals with the bounds of a unified integral operator with which several fractional
and conformable integral operators are directly associated. By using quasiconvex and …

Derivation of bounds of several kinds of operators via -convexity

Y Chel Kwun, G Farid, S Min Kang… - Advances in Difference …, 2020 - Springer
The objective of this paper is to derive the bounds of fractional and conformable integral
operators for (s, m) (s,m)-convex functions in a unified form. Further, the upper and lower …

Certain new Chebyshev and Grüss-type inequalities for unified fractional integral operators via an extended generalized Mittag-Leffler function

W Yang - Fractal and Fractional, 2022 - mdpi.com
In this paper, by adopting the classical method of proofs, we establish certain new
Chebyshev and Grüss-type inequalities for unified fractional integral operators via an …

On generalized strongly convex functions and unified integral operators

T Yu, G Farid, K Mahreen, CY Jung… - Mathematical Problems …, 2021 - Wiley Online Library
In this paper, we define a strongly exponentially (α, h− m)‐convex function that generates
several kinds of strongly convex and convex functions. The left and right unified integral …

New refinements of Chebyshev–Pólya–Szegö-type inequalities via generalized fractional integral operators

SI Butt, AO Akdemir, MY Bhatti, M Nadeem - Journal of Inequalities and …, 2020 - Springer
Fractional analysis, as a rapidly developing area, is a tool to bring new derivatives and
integrals into the literature with the effort put forward by many researchers in recent years …

Grüss type inequalities via generalized fractional operators

SI Butt, AO Akdemir, M Nadeem… - … Methods in the Applied …, 2021 - Wiley Online Library
One of the main motivation points in studies on inequalities is to obtain generalizations and
to introduce new approaches. In this direction, the generalized fractional integral operators …