Fixed point theorems and T-stability of Picard iteration for generalized Lipschitz mappings in cone metric spaces over Banach algebras

摘要

In this paper, we obtain the existence of non-normal solid cone and some fixed point theorems for generalized Lipschitz contractive mappings in cone metric spaces over Banach algebras. Our results greatly generalize the main work by Xu and Radenovie (Fixed Point Theory and Applications, 2014, 2014: 102). Moreover, we verify the P property and T-stability of Picard's iteration. Further, we give an example to illustrate that our works are never a copy of metric results in the literature.