The notion of mixed quermassintegrals in the classical Brunn-Minkowski theory is extended to that of Orlicz mixed quermassintegrals in the Orlicz Brunn-Minkowski theory. The analogs of the classical Cauchy- Kuhota for...The notion of mixed quermassintegrals in the classical Brunn-Minkowski theory is extended to that of Orlicz mixed quermassintegrals in the Orlicz Brunn-Minkowski theory. The analogs of the classical Cauchy- Kuhota formula, the Minkowski isoperimetric inequality and the Brunn-Minkowski inequality are established for this new Orlicz mixed quermassintegrals.展开更多
We prove some analogs inequalities of the logarithmic Minkowski inequality for general nonsymmetric convex bodies. As applications of one of those inequalities, the p-affine isoperimetric inequality and some other ine...We prove some analogs inequalities of the logarithmic Minkowski inequality for general nonsymmetric convex bodies. As applications of one of those inequalities, the p-affine isoperimetric inequality and some other inequalities are obtained.展开更多
This paper introduces and considers a new system of generalized mixed variational inequal- ities in a Hilbert space, which includes many new and known systems of variational inequalities and generalized variational in...This paper introduces and considers a new system of generalized mixed variational inequal- ities in a Hilbert space, which includes many new and known systems of variational inequalities and generalized variational inequalities as special cases. By using the two concepts of η-subdifferential and η-proximal mappings of a proper function, the authors try to demonstrate that the system of generalized mixed variational inequalities is equivalence with a fixed point problem. By applying the equivalence, a new and innovative η-proximal point algorithm for finding approximate solutions of the system of generalized mixed variational inequalities will be suggested and analyzed. The authors also study the convergence analysis of the new iterative method under much weaker conditions. The results can be viewed as a refinement and improvement of the previously known results for variational inequalities.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11001163)Innovation Program of Shanghai Municipal Education Commission(Grant No.11YZ11)
文摘The notion of mixed quermassintegrals in the classical Brunn-Minkowski theory is extended to that of Orlicz mixed quermassintegrals in the Orlicz Brunn-Minkowski theory. The analogs of the classical Cauchy- Kuhota formula, the Minkowski isoperimetric inequality and the Brunn-Minkowski inequality are established for this new Orlicz mixed quermassintegrals.
基金supported by National Natural Science Foundation of China(Grant Nos.11671325 and 11401486)the Natural Science Foundation Project of CQ CSTC(Grant No.cstc2016jcyj A0465)
文摘We prove some analogs inequalities of the logarithmic Minkowski inequality for general nonsymmetric convex bodies. As applications of one of those inequalities, the p-affine isoperimetric inequality and some other inequalities are obtained.
基金supported by the Natural Science Foundation of China under Grant No.11001287the Natural Science Foundation Project of CSTC under Grant No.2010BB9254
文摘This paper introduces and considers a new system of generalized mixed variational inequal- ities in a Hilbert space, which includes many new and known systems of variational inequalities and generalized variational inequalities as special cases. By using the two concepts of η-subdifferential and η-proximal mappings of a proper function, the authors try to demonstrate that the system of generalized mixed variational inequalities is equivalence with a fixed point problem. By applying the equivalence, a new and innovative η-proximal point algorithm for finding approximate solutions of the system of generalized mixed variational inequalities will be suggested and analyzed. The authors also study the convergence analysis of the new iterative method under much weaker conditions. The results can be viewed as a refinement and improvement of the previously known results for variational inequalities.
