Erhan Set

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 some inequalities of Hermite–Hadamard type via m-convexity

Abstract In this paper we give some estimates to the right-hand side of Hermite–Hadamard inequality for functions whose absolute values of second derivatives raised to positive real powers are m -convex.

OSTROWSKI’S TYPE INEQUALITIES FOR (ALPHA, M)-CONVEX FUNCTIONS

In this paper, we establish new inequalities of Ostrowskis type for functions whose derivatives in absolute value are (, m)-convex.

On the Hermite-Hadamard Inequality and Other Integral Inequalities Involving Two Functions

We establish some new Hermite-Hadamard-type inequalities involving product of two functions. Other integral inequalities for two functions are obtained as well. The analysis used in the proofs is fairly elementary and based on the use of the Minkowski, Hölder, and Young inequalities.

On Hadamard-Type Inequalities Involving Several Kinds of Convexity

We do not only give the extensions of the results given by Gill et al. (1997) for log-convex functions but also obtain some new Hadamard-type inequalities for log-convex -convex, and -convex functions.

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.

On generalized Grüss type inequalities for k-fractional integrals

The aim of the present paper is to investigate some new integral inequalities of Gruss type for k?-?Riemann-Liouville fractional integrals. From our results, new weighted or classical Gruss type inequalities have been established for some special cases. Moreover, special cases of the integral inequalities in this paper have been obtained by Dahmani and Tabharit, 2010 in 5.

On some inequalities for s-convex functions and applications

Some new results related to the left-hand side of the Hermite-Hadamard type inequalities for the class of functions whose second derivatives at certain powers are s-convex functions in the second sense are obtained. Also, some applications to special means of real numbers are provided.MSC:26A51, 26D15.

On the generalization of Ostrowski and Grüss type discrete inequalities

Abstract The main purpose of this paper is to establish a generalization of discrete inequalities of the Ostrowski and Gruss type involving two functions. The analysis used in the proofs is fairly elementary.