Some generalized inequalities for double integrals and applications

The main purpose of the thesis is to establish new Hermite-Hadamard type and Ostrowski type inequalities for co-ordinated convex or different type bounded functions by using double integals. In section 3, it is established an identity for second order partial derivative functions. Then, new inequalities of Ostrowski type for double integrals is obtained by using this identity. Also, some applications of these Ostrowski type inequalities connected to the Cubature formula are given. Finally, it is investigated some inequalities of Hermite-Hadamard type for double integrals of functions whose partial derivatives in absolute value are convex on the co- ordinates on rectangle from the plane. In section 4, it is given new some generalized weighted integral inequalities for convex functions on the co-ordinates defined in a rectangle from the plane. These results are generalized to some recent results obtained for functions whose partial derivatives in absolute value are convex on the co-ordinates on the rectangle from the plane. In section 5, it is established weighted Ostrowski type inequalities involving higher-order partial derivatives by using two dimensional integrals on Lebesgue spaces. Then, these results are applied to the Cubature formula. Additionally, by the help of these inequalities, it is presented some applications based on the moments of random variables. Finally, it is obtained some Hadamard type inequalities for double integrals of functions whose higher-order partial derivatives in absolute value are co-ordinated convex functions.