پديد آورنده :
كراري، سميرا سادات
عنوان :
نامساوي هرون و نامساوي يانگ براي ماتريس ها
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان : دانشگاه صنعتي اصفهان
استاد راهنما :
محمود منجگاني
استاد مشاور :
فريد بهرامي
توصيفگر ها :
ميانگين هرون , نامساوي يانگ , نامساوي عملگري , نرم پايدار يكاني
استاد داور :
مهدي نعمتي.سيما سلطاني
تاريخ ورود اطلاعات :
1399/10/07
تاريخ ويرايش اطلاعات :
1400/09/10
چكيده انگليسي :
Heron s inequality and Yoing s inequality for Matrices Samira Sadat Karrari September 18 2020 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Seyed Mahmoud Manjegani manjgani@iut ac ir2000 MSC 15A15 15A42 15A60 47A30Keywords Heron mean Young s inequality Operator inequality Unitarily invariant normAbstract The aim of this dissertation is introduce and study of some improvements of Heron mean and the refinements ofYoung s inequalities for matrices This dissertation is written based on article Some results of Heron mean andYoung s inequalities Changsen and Yonghui Ren 2018 For two positive real number a b and 0 1 the equality a b F a b 1 ab 2is called Heron mean The inequality a b1 a 1 b 1is called Young s inequality if 2 then the above inequality is called arithmetic geometric means inequality Heron mean inequality is the interpolation between arithmetic and geometric mean The first refinements of Young s inequality was shown by Kittaneh and Manasrah in 2010 as follow a b 1 2 min 1 2 a b 2 a 1 b 2 Later they obtained other interesting refinements Bhatia and Kittaneh in 1990 noted that a version of arithmetic geometric mean inequality in the case 1 for 2singular values of matrices Motivated by the Bhatia and Kittaneh method Ando in 1995 consider Young s inequalityfor any 0 1 and prove that for any two n n matrices A B 1 sj AB sj A 1 B 1 1 1 j n The Hilbert Schmidt norm of A aij Mn is defined by n A 2 aij 2 i j 1and is unitary invariant norm in the sense that for all unitary matrices U V M U AV A We usethe following notations A B 1 A B 0 1 A B A 2 A 2 BA 2 A 2 R 1 1 1 1denoted by A B and A B when 1 2In the first chapter of this dissertation provide the inequalities for real numbers and their refinement In chapter two the necessary background in matrix theory is presented In chapter three Young s inequality and Heron inequalityfor matrices are studied The main results are as follow
استاد راهنما :
محمود منجگاني
استاد مشاور :
فريد بهرامي
استاد داور :
مهدي نعمتي.سيما سلطاني
