Estimation-type results on the k-fractional Simpson-type integral inequalities and applications

Abstract

ABSTRACTWe establish a Simpson-type identity of multiparameter and certain Simpson-type inequalities via k-fractional integrals. Worth mentioning, the obtained inequalities in this article generalize some results presented by Set et al. [Simpson type integral inequalities for convex functions via Riemann-Liouville integrals. Filomat. 2017;31(14):4415–4420] and Sarikaya et al. [On new inequalities of Simpson's type for s-convex functions. Comput Math Appl. 2010;60:2191–2199]. As applications, we also provide several inequalities for f-divergence measures and probability density functions. We expect that this study will be result in the new k-fractional integration explorations for Simpson-type inequalities.