Co-ordinated Convex Functions Research Articles

Integral inequalities for (Orlicz, Breckner) co-ordinated convex functions on rectangles

Abstract The concept of (Orlicz, Breckner) co-ordinated (s, σ)-convexity is introduced for two variables real functions. Upper and lower sharp integral boundary properties of Hermite-Hadamard type are proved on rectangles.

Some new Hermite–Hadamard type inequalities for differentiable co-ordinated convex functions

AbstractIn the paper, the authors establish some new Hermite–Hadamard type inequalities for differentiable co-ordinated convex functions of two variables.

On Some Integral Inequalities Related to Hermite-Hadamard-Fejér Inequalities for Coordinated Convex Functions

Several new mappings associated with coordinated convexity are proposed, by which we obtain some new Hermite-Hadamard-Fejér type inequalities for coordinated convex functions. We conclude that the results obtained in this work are the generalizations of the earlier results.

New inequalities for co-ordinated convex functions via Riemann-Liouville fractional calculus

We provide some new Hermite-Hadamard type inequalities for co-ordinated convex functions, via Riemann-Liouville fractional integration.

On the Co-Ordinated Convex Functions

In this paper, some new integral inequalities are given for convex functions on the co-ordinates. By using well-known classical inequalities and a new integral identity (Lemma 1), we obtain some general results for co-ordinated convex functions.

Generalizations of Inequalities for Differentiable Co-Ordinated Convex Functions

A generalized lemmas is proved and several new inequalities for differentiable co-ordinated convex and concave functions in two variables are obtained.

Some Hermite-Hadamard Type Inequalities for Differentiable Co-Ordinated Convex Functions and Applications

In this paper, we shall establish an inequality for differentiable co-ordinated convex functions on a rectangle from the plane. It is connected with the left side and right side of extended Hermite-Hadamard inequality in two variables. In addition, six other inequalities are derived from it for some refinements. Finally, this paper shows some examples that these inequalities are able to be applied to some special means.

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.

On some FEJÉR-type inequalities for double integrals

In this paper some new Fej\'{e}r-type inequalities are established for co-ordinated convex functions.

On some new inequalities for differentiable co-ordinated convex functions

Several new inequalities for differentiable co-ordinated convex and concave functions in two variables which are related to the left side of Hermite- Hadamard type inequality for co-ordinated convex functions in two variables are obtained. Mathematics Subject Classification (2000): 26A51; 26D15

Inequalities for convex and s-convex functions on Δ = [a, b] × [c, d

Abstract In this article, two new lemmas are proved and inequalities are established for co-ordinated convex functions and co-ordinated s-convex functions. Mathematics Subject Classification (2000): 26D10; 26D15.