SOME EXTENDED TRAPEZOID-TYPE INEQUALITIES AND APPLICATIONS

Some extended Simpson-type inequalities and applications

‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.

Some Inequalities of Perturbed Trapezoid Type

A new generalized perturbed trapezoid type inequality is established by Peano kernel approach. Some related results are also given.

Extended Hardy-littlewood Inequalities and Some Applications

We establish conditions under which the extended Hardy-Littlewood inequality ∫ RN H ( |x|, u1(x), . . . , um(x) ) dx ≤ ∫ RN H ( |x|, u1(x), . . . , um(x) ) dx, where each ui is non-negative and u ∗ i denotes its Schwarz symmetrization, holds. We also determine appropriate monotonicity assumptions on H such that equality occurs in the above inequality if and only if each ui is Schwarz symmetric....

Weighted Ostrowski, Trapezoid and Grüss Type Inequalities on Time Scales

In this paper we first derive a weighted Montgomery identity on time scales and then establish weighted Ostrowski, trapezoid and Grüss type inequalities on time scales, respectively. These results not only provide a generalization of the known results, but also give some other interesting inequalities on time scales as special cases.

Some Grüss Type Inequalities for Riemann-stieltjes Integral and Applications