On weighted Iyengar-type inequalities for conformable fractional integrals

The presence of a differentiable mappings was introduced in 1938 for the first time and the results were announced by Iyengar. In recent years, Iyengar-type integral inequalities have been studied by several authors such as [5, 6, 9, 10, 12]. In this paper, we concentrate on Iyengar-type integral inequalities and present some generalizations. Section 2 consists of conformable integrals, derivatives, and some properties of them. Steffensen’s inequality for conformable fractional integral is also given. Finally, in Sect. 3, my means of Steffensen’s inequality, we obtain some main interesting results. We first establish two new identities for conformable integral involving some moments. Generalizing this, using these equalities and considering fractional Steffensen’s inequality for conformable fractional integrals, we get a new version of weighted Iyengar-type integral inequalities for conformable integrals. The results presented here will provide generalizations of those given in earlier works. Iyengar proved a useful inequality which gives an upper bound for the approximation of the integral average by the mean of the values of mapping at end points of the interval that is given below (see [7] or [11, p.471]).