The Matrix Analogs of Firey’s Extension of Minkowski Inequality and of Firey’s Extension of Brunn-Minkowski Inequality
نویسندگان
چکیده
– The Brunn-Minkowski theory is a central part of convex geometry. At its foundation lies the Minkowski addition of convex bodies which led to the definition of mixed volume of convex bodies and to various notions and inequalities in convex geometry. Its origins were in Minkowski’s joining his notion of mixed volumes with the Brunn-Minkowski inequality, which dated back to 1887. Since then it has led to a series of other inequalities in convex geometry. The existence is very useful and widely used in mathematical and engineering applications. Our purpose of this series was to develop an equivalent series of inequalities for positive definite symmetric matrices. The major theorems presented here are the matrix analogs of Firey’s extension of Minkowski inequality and of Firey’s extension of Brunn-Minkowski inequality. Key-Words: – Aleksandrov inequality, Quermassintegral, Mixed Quermassintegral, Matrix Firey p-Sum, Mixed p-Quermassintegral, matrix analog of Firey’s Extension of Brunn-Minkowski inequality, matrix analog of Firey’s Extension of Minkowski inequality
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