Fixed point theorems of contractive mappings in cone b-metric spaces and applications

By Huaping Huang, Shaoyuan Xu. Fixed Point Theory and Applications, 2013

105 citations recorded by the source corpus.

In this paper we present some new examples in cone b-metric spaces and prove some fixed point theorems of contractive mappings without the assumption of normality in cone b-metric spaces. The results not only directly improve and generalize some fixed point results in metric spaces and b-metric spaces, but also expand and complement some previous results in cone metric spaces. In addition, we use our results to obtain the existence and uniqueness of a solution for an ordinary differential equation with a periodic boundary condition.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ac92d05ef94e2f2276ce2b86030b1656512e8a72

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In Geometry and Topology

Citations in the corpus

Some Equivalences between Cone $b$-Metric Spaces and $b$-Metric Spaces (2013, result): “Now, we show that main results in [9] are consequences of preceding results on b-metric spaces.”
EXISTENCE OF FIXED POINTS OF SET-VALUED MAPPINGS IN b-METRIC SPACES (2016, unknown): “[1, 3, 4, 5, 9, 13, 14, 15, 16, 24, 26, 27] and related references therein.”
Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications (2015, background): “A large number of works are noted in [1, 2, 3, 8, 11, 12, 15, 17, 18, 20] and the relevant literature therein.”