M. Emin Özdemir

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.

New inequalities of hermite-hadamard type for convex functions with applications

In this paper, some new inequalities of the Hermite-Hadamard type for functions whose modulus of the derivatives are convex and applications for special means are given. Finally, some error estimates for the trapezoidal formula are obtained.2000 Mathematics Subject Classiffication. 26A51, 26D10, 26D15.

New inequalities of Hermite–Hadamard type via s-convex functions in the second sense with applications

Abstract In this paper, we establish some new inequalities of Hermite–Hadamard type whose derivatives in absolute value are s-convex in the second sense. Finally some applications to special means of positive real numbers are given.

Hermite-Hadamard-type inequalities via (α,m)-convexity

In this paper, we establish several new inequalities for functions whose second derivative in absolute value aroused to the qth(q>=1) power are (@a,m)-convex. Some applications to special means of positive real numbers are also given.

A theorem on mappings with bounded derivatives with applications to quadrature rules and means

In this paper, we establish a new inequality of Theorem 2 [Appl. Math. Lett. 13 (2000) 19] (Dragomirs integral inequality) for functions whose derivatives are bounded. This has immediate applications in numerical integration where new estimates are obtained for the remainder term of the trapezoid, mid-point. Some natural applications to special means of real numbers are given. For several recent results concerning Dragomirs integral inequality (see [Appl. Math. Lett. 13 (2000) 19] where further references are listed).

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 new inequalities of Hermite-Hadamard-Fejér type for convex functions via fractional integrals

In this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite-Hadamard-Fejer type integral inequality. The results presented here would provide extensions of those given in earlier works.

Two new theorem on mappings uniformly continuous and convex with applications to quadrature rules and means

An interesting connection exists between convex functions and uniformly continuous functions. This linkage leads to some interesting functional inequalities over the open interval which works well in quadrature rules and means. In this paper, we establish two new theorem which connect the Hermite-Hadamard type functions.

THE HERMITE-HADAMARD'S INEQUALITY FOR SOME CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS AND RELATED RESULTS

Abstract In this paper, we establish Hermite-Hadamard type inequalities for s - convex functions in the second sense and m - convex functions via fractional integrals. The analysis used in the proofs is fairly elementary.

Some Ostrowski’s type inequalities for functions whose second derivatives are s-convex in the second sense

Abstract Some new inequalities of the Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are given