On Newton type inequalities associated with the generalized fractional integrals via various function classes

Abstract

In this paper, we investigate Newton-type inequalities for different classesof functions using generalized fractional integral operators defined bySarikaya and Ertu\u{g}ral in \cite{sarikaya}. In particular, Newton-typeinequalities involving generalized fractional integral are obtained fordifferentiable convex functions. Then, similar inequalities are proved forbounded functions and Lipschitz functions. In addition, Newton typeinequalities for functions with bounded variation are presented.Furthermore, we emphasize that the results of this study generalize theinequalities established in previous research for classical Riemann integraland Riemann-Liouville fractional integrals. Furthermore, as special cases ofmain results, we present several Newton-type inequalities for $k$%-Riemann-Liouville fractional integrals.