In this paper, using a general class of fractional integral operators, we establish new fractional integral inequalities of Hermite-Hadamard type. The main results are used to derive Hermite-Hadamard type inequalities involving the familiar Riemann-Liouville fractional integral operators.

In this paper, using fractional integration, we present new fractional integral inequalities related to Holder inequality.We generalise a Wu's sharpness of Holder inequality for p, q integration.Then, as an application, we propose another way to derive the Holder inequality which is already established by Z. Dahmani on 2012 in General Math.Journal.Also, for our results, the classical Holder inequality is deduced as a special case.MSC 2010.26D15, 26A33, 60E15.

In this paper, we give new definitons related to Katugampola fractional integral for two variables functions. We are interested in giving the Hermite-Hadamard inequality for a rectangle in plane via convex functions on co-ordinates involving Katugampola fractional integral.

In this paper, we extend the Montgomery identities for the generalized fractional integrals. These results are connected with the celebrated Ostrowski type integral inequality for generalized fractional integral operators by definition of Sarikaya et al.[6]. The results presented here would provide extensions of those given in earlier works.

The aim of this paper is to the Hermite-Hadamard type inequalities for functions whose first derivatives in absolute value is s-convex through the instrument of generalized Katugampola fractional integrals.

In this paper, we have established the left hand side of the Hermite-Hadamard-Fejer type inequalities for the class of functions whose derivatives in absolute value at certain powers are convex functions by using fractional integrals.

In this paper, using Riemann-Liouville integral operators, we establish new fractional in- tegral inequalities of Hermite-Hadamard-Fejer type for co-ordinated convex functions on a rectangle of R^2. The results presented here would provide extensions of those given in earlier works.

In this paper, we use techniques and tools from time scale calculus to state and prove many refinements on the discrete Hermite–Hadamard inequality.

AbstractIn the present work, we give the definition of an

In this study, we establish some new weighted Iyengar-type integral inequalities using fractional Steffensen’s inequality for conformable fractional integral. The results presented here would provide generalizations of those given in earlier works.

The aim of this paper is to establish some Steffensen’s type inequalities for conformable fractional integral. The results presented here would provide generalizations of those given in earlier works.

In this paper, we introduce the definition of a convex real valued function f defined on the set of integers, Z. We prove that f is convex on Z if and only if Delta(2)f >= 0 on Z. As a first application of this new concept, we state and prove discrete Hermite-Hadamard inequality using the basics of discrete calculus (i.e., the calculus on Z). Second, we state and prove the discrete fractional Hermite-Hadamard inequality using the basics of discrete fractional calculus. We close the paper by defining the convexity of a real valued function on any time scale.

In this paper, we extend the Hermite-Hadamard-type inequality and Jensen-type inequality for convex stochastic proceses. The generalization of Hermite- Hadamard-type inequality for convex stochastic proceses is also obtained and some special cases of this result are given.

In this paper, some perturbed companion of Ostrowski type integral inequalities for functions whose second derivatives are either bounded or of bounded variation are established.

In this paper, a version of Hermite Hadamard-type inequalities for (d, t)-convex functions are established. And then we give some new inequalities of the Hermite-Hadamard type for the product of two (d, t)-convex functions.

In this paper, we obtain new identity for function of two variables and apply them to give new Ostrowski type integral inequality for double integrals involving functions whose derivatives are co-ordinates convex function on ( ) ( ) :, , ab c d ∆= × in 2 R with , a b c d << .

In this paper, new integral inequalities of Hadamard type involving several differentiable Φ-r-convex functions are given.

In this paper, we obtain weighted Ostrowski type inequalities for function whose second order partial derivatives are bounded.

In this paper, we extend some estimates of the right-hand side of a Hermite–Hadamard–Fejér type inequality for functions whose first derivatives’ absolute values are convex. The results presented here would provide extensions of those given in earlier works.

In this paper, some generalization integral inequalities of Hermite-Hadamard type for functions whose derivatives are convex in modulus are given by using fractional integrals.