AROUND PEROV'S FIXED POINT THEOREM FOR MAPPINGS ON GENERALIZED METRIC SPACES

作者：Jachymski Jacek^*; Klima Jakub

来源：Fixed Point Theory, 2016, 17(2): 367-380.

• Generalized metric space
• Perov's fixed point theorem
• K-metric space
• cone metric space
• spectral radius
• Cauchy initial value problem
• solid cone
• normal cone
• nonlinear Lipschitz condition

We revisit Perov's fixed point theorem for selfmaps of a set endowed with a vector metric taking values in the Euclidean space R-m. In particular, we show that this result is subsumed by the classical Banach contraction principle. We also obtain a generalization of Perov's theorem by considering mappings on K-metric spaces satisfying a nonlinear Lipschitz condition. Two applications are presented and some characterizations of convergence in K-metric spaces are given.

• 出版日期2016