The Generalized Inequalities via Means and Positive Linear Mappings
عنوان مقاله: The Generalized Inequalities via Means and Positive Linear Mappings
شناسه ملی مقاله: JR_SCMA-19-2_009
منتشر شده در در سال 1401
شناسه ملی مقاله: JR_SCMA-19-2_009
منتشر شده در در سال 1401
مشخصات نویسندگان مقاله:
Leila Nasiri - Department of Mathematics and computer science, Faculty of science, Lorestan University, Khorramabad, Iran.
Mehdi Shams - Department of Statistics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran.
خلاصه مقاله:
Leila Nasiri - Department of Mathematics and computer science, Faculty of science, Lorestan University, Khorramabad, Iran.
Mehdi Shams - Department of Statistics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran.
In this paper, we establish further improvements of the Young inequality and its reverse. Then, we assert operator versions corresponding them. Moreover, an application including positive linear mappings is given. For example, if A,B\in {\mathbb B}({\mathscr H}) are two invertible positive operators such that ۰\begin{align*}& \Phi ^{۲} \bigg(A \nabla _{\nu} B+ rMm \left( A^{-۱}+A^{-۱} \sharp_{\mu} B^{-۱} -۲ \left(A^{-۱} \sharp_{\frac{\mu}{۲}} B^{-۱} \right)\right)\\& \qquad +\left(\frac{\nu}{\mu} \right) Mm \bigg(A^{-۱}\nabla_{\mu} B^{-۱} -A^{-۱} \sharp_{\mu} B^{-۱}\bigg)\bigg) \\& \quad \leq \left( \frac{K(h)}{ K\left( \sqrt{{h^{'}}^{\mu}},۲ \right)^{r^{'}}} \right) ^{۲} \Phi^{۲} (A \sharp_{\nu} B),\end{align*}where r=\min\{\nu,۱-\nu\}, K(h)=\frac{(۱+h)^{۲}}{۴h}, h=\frac{M}{m}, h^{'}=\frac{M^{'}}{m^{'}} and r^{'}=\min\{۲r,۱-۲r\}. The results of this paper generalize the results of recent years.
کلمات کلیدی: Operator means, Numerical means, Kantorovich's constant, Positive linear map
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1555091/