Mehmet Zeki Sarikaya

On new inequalities of Simpson's type for s-convex functions

In this paper, we establish some new inequalities of Simpsons type based on s-convexity. Some applications to special means of real numbers are also given.

On the generalization of some integral inequalities and their applications

Abstract In this paper, a general integral identity for convex functions is derived. Then, we establish some new inequalities of the Simpson and the Hermite–Hadamard type for functions whose absolute values of derivatives are convex. Some applications for special means of real numbers are also provided.

ON NEW INEQUALITIES VIA RIEMANN-LIOUVILLE FRACTIONAL INTEGRATION

We extend the Montgomery identities for the Riemann-Liouville fractional integrals. We also use these Montgomery identities to establish some new integral inequalities. Finally, we develop some integral inequalities for the fractional integral using differentiable convex functions.

Extensions of certain integral inequalities on time scales

Abstract In this work, we establish Holder’s inequality, Minkowski’s inequality and Jensen’s inequality on time scales via the nabla integral and diamond- α dynamic integral, which is defined as a linear combination of the delta and nabla integrals.

New Inequalities of Hermite-Hadamard Type for Functions Whose Second Derivatives Absolute Values Are Convex and Quasi-Convex

In this paper, we establish several new inequalities for twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

Some New Inequalities of Hermite-Hadamard`s Type

In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

ON THE OSTROWSKI TYPE INTEGRAL INEQUALITY FOR DOUBLE INTEGRALS

Abstract In this note, we establish a new inequality of Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.

INEQUALITIES OF HERMITE‐HADAMARD TYPE FOR FUNCTIONS WHOSE DERIVATIVES ABSOLUTE VALUES ARE m‐CONVEX

In this paper, we establish several inequalities of Hermite‐Hadamard type for functions whose derivatives absolute values are m‐convex.

On the Hermite–Hadamard-type inequalities for co-ordinated convex function via fractional integrals

In this paper, we initially present new some inequality of Hermite–Hadamard-type for co-ordinated convex functions on a rectangle from the plane ℝ2 via Riemann–Liouville fractional integrals. Then, we give an integral identity for fractional integrals and with the help of this integral identity we establish some integral inequalities with the right-hand side of the fractional Hermite–Hadamard-type inequality on the co-ordinates.

New weighted Ostrowski and Čebyšev type inequalities on time scales

In this study, we establish some new weighted inequalities of Ostrowski and Cebysev type involving two functions on time scales. Our proofs are of independent interest and provide new estimates on these types inequalities.