标题： 加权情况下的数值半径、Crawford数和数值指标函数的推广 显示英文标题

标题： Generalizations of the Numerical Radius, Crawford Number and Numerical Index Functions in the Weighted Case

摘要： 在本文中，首先研究了加权数值半径和加权Crawford数函数的一些简单和光滑性质。 然后，得到了加权数值半径函数的下界和上界的广义公式。 随后，给出了加权数值指标的下界和上界的某些估计。 所得结果推广了近期文献中关于特殊加权数值半径和特殊加权Crawford数函数的一些著名结果。 此外，还为文献提供了不同且有用的结果。 显示英文摘要

摘要： In this article, firstly, some simple and smoothness properties of the weighted numerical radius and the weighted Crawford number functions are investigated. Then, some generalization formulas for lower and upper bounds of the weighted numerical radius function are obtained. Later on, some evaluations for lower and upper bounds of the weighted numerical index are given. The obtained results are generalized some well-known famous results about the special weighted numerical radius and the special weighted Crawford number functions in the recently literature. Also, the different and useful results are provided to the literature.