In this paper, we establish some relations between the Hilbert＇s projective metric and the norm on a Banach space and show that the metric and the norm induce equivalent convergences at certain set. As applications, ...In this paper, we establish some relations between the Hilbert＇s projective metric and the norm on a Banach space and show that the metric and the norm induce equivalent convergences at certain set. As applications, we utilize the main results to discuss the eigenvalue problems for a class of positive homogeneous operators of degree a and the positive solutions for a class of nonlinear algebraic system.展开更多
基金Supported by the Natural Science Foundation of Shanxi Province (Grant No.20041003)the Youth Science Foundation of Shanxi Province (Grant No.2010021002-1)
文摘In this paper, we establish some relations between the Hilbert＇s projective metric and the norm on a Banach space and show that the metric and the norm induce equivalent convergences at certain set. As applications, we utilize the main results to discuss the eigenvalue problems for a class of positive homogeneous operators of degree a and the positive solutions for a class of nonlinear algebraic system.
