Exploring An Extension Of Grand Further Inequality By Mean Theoretic Approach And The Application Of Choi Inequality

Throughout this paper, we pay our attention to the Furuta inequality and the grand Puruta inequality, we will further research some inequalities about more operators by con-sidering a mean theoretic approach; In The last chapter, we introduce the application of Choi inequality.The first chapter describes the relevant background knowledge and briefly introduces some important theorems.The second chapter uses a lemma, i.e:Let A≥B≥0with A>0. Then A≥B≥(At(?)β-t/p-tBp)1/β) holds for t∈[0,1],β≥p≥1and p#t.In this chapter, we show an extension about several operators and related deforma-tions.The third chapter is an important part of this paper, we use Furuta inequality to obtain a further extension about more operators based on the weighted geometric mean and obtain two important inequalities. In addition, we give some variants of the former chapter and show their related corollaries.Finally, we apply Choi inequality to get some theorems and their related corollaries.