Inequalities For The Double Chord-power Integral

Inequalities are always the very active field of research and appealing in mathematics. Geometric inequalities have their own unique characteristics and charm theory, the classical isopcrimefric inequalities arc still intriguing. The chord-integral inequalities are the development and summary of isoperimetric inequalities and the important contents of integral geometry and related disciplines. Their application of convex body and geometry probability is the important theory in integral geometry and convex geometry, One can study the geometric invariants and geometric probability and other issues.Based the new definition of double chord-power intergral which the pair of lines intersect the convex body in integral geometry, this paper studies the relationship of double chord-power intergral and chord-power intergral. And the special inferior double chord-power intergrals are calculated using kinds of integral methods. Since there is natural different of the kinematic density formula for pairs of intersecting lines in two-dimensional surface and three-dimensional space, the inequalities for double chord-power integrals have studied from two side of two-dimensional surface and three-dimensional space using chord-power intergral inequality. Schwarz inequality. Holder inequality and so on. Finally this paper showed the application of double chord-power integral inequality from the geometry probability.By studying double-power integral, the geometric invariants and geometric probability can studied from the perspective. In particular, more complicated geometric probability can be resolved with the double-power integral inequality. These inequalities have further developed the chord-power integral theory and have provided the new theory and method to the correlation field research. This theory system will pour into the new vigor to the integral geometry and the geometry probability, provides the new theory basis for the integral geometry and the geometry probability.