Inequalities for a unified integral operator via \((\alpha,m)\)-convex functions (Q2194656)

Summary: Recently, a unified integral operator has been introduced by \textit{G. Farid} [``A unified integral operator and further its consequences'', Open J. Math. Anal. 4, No. 1, 1--7 (2020; \url{doi:10.30538/psrp-oma2020.0047})], which produces several kinds of known fractional and conformable integral operators defined in recent decades (\textit{Y. C. Kwun} et al. [``Inequalities for a unified integral operator and associated results in fractional calculus'', IEEE Access 7, 126283--126292 (2019; \url{doi:10.1109/ACCESS.2019.2939166})], Remarks 6 and 7). The aim of this paper is to establish bounds of this unified integral operator by means of \((\alpha,m)\)-convex functions. The resulting inequalities provide the bounds of all associated fractional and conformable integral operators in a compact form. Also, the results of this paper hold for different kinds of convex functions connected with \((\alpha,m)\)-convex functions.