In this paper, we obtained some new estimates on generalization of Hadamard, Ostrowski and Simpson-like type inequalities for harmonically quasi-convex functions via Riemann Liouville fractional integral.

In this paper we obtain sharp Ostrowski type inequalities for multidimensional sets of bounded variation and multivariate functions of bounded variation.

In the present paper, the notion of generalized $(r;g,s,m,varphi)$-preinvex function is applied to establish some new generalizations of Ostrowski type integral inequalities via Caputo $k$-fractional derivatives. At the end, some applications to special means are given.

In this paper, we have obtained weighted versions of Ostrowski, Čebysev and Grüss type inequalities for conformable fractional integrals which is given by Katugompola. By using the Katugampola definition for conformable calculus, the present study confirms previous findings and contributes additional evidence that provide the bounds for more general functions.

In this paper, we establish a new integral identity involving differentiable functions, and then use the newly established to prove some Ostrowski–Mercer-type inequalities for convex functions. It is also demonstrated that are generalizations of Ostrowski inside literature. There applications special means real numbers given.

An Ostrowski type inequality for general convex functions defined on linear spaces is generalised. Some inequalities which improve the HermiteHadamard type inequality for convex functions defined on linear spaces are derived using the obtained result. The results in normed linear spaces are used to obtain some inequalities which are related to the given norm and associated semi-inner products, ...

Motivated by the work of George A. Anastassiou in [George A. Anastassiou, Ostrowski and Landau inequalities for Banach space valued functions, Mathematical and Computer Modelling, 55 (2012), 312–329], we derive some Landau type inequalities for Banach space valued functions without assuming the boundary conditions.

Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remaiders. Then we derive related discrete nabla fractional Opial, Ostrowski, Poincaré and Sobolev type inequalities .