Some Additive Inequalities for Heinz Operator Mean

Authors : Sever DRAGOMİR

Pages : 168-174

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Publication Date : 2019-04-15

Article Type : Research Paper

Abstract :In this paper we obtain some new additive inequalities for Heinz operator mean, namely the operator $H_{\nu }\leftinsert ignore into journalissuearticles values( A,B\right); :=\frac{1}{2}\leftinsert ignore into journalissuearticles values( A\sharp _{\nu }B+A\sharp _{1-\nu }B\right); $ where $A\sharp _{\nu }B:=A^{1/2}\leftinsert ignore into journalissuearticles values( A^{-1/2}BA^{-1/2}\right); ^{\nu }A^{1/2}$ is the weighted geometric mean for the positive invertible operators $A$ and $B,$ and $\nu \in \left[ 0,1\right] .$
Keywords : Young’s Inequality, Real functions, Arithmetic mean Geometric mean inequality