Common fixed point theorems for cyclic contractive mappings in partial cone b-metric spaces and applications to integral equations

• DOI: 10.15388/na.2016.6.5
• Publication Date: 2016-12-18T22:47:24Z
• Authors: Chuanxi Zhu; Wenqing Xu; Tatjana Došenovič; Zorana Golubovic
• Keywords: Cone (formal languages); Coincidence point

In this paper, we introduce the concept of partial cone b-metric spaces as a generalization of partial metric, cone metric and b-metric spaces and establish some topological properties of partial cone b-metric spaces. Moreover, we also prove some common fixed point theorems for cyclic contractive mappings in such spaces. Our results generalize and extend the main results of Huang and Zhang [Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332:1468–1476, 2007], Stanić et al. [Common fixed point under contractive condition of Ćirić's type on cone metric type spaces, Fixed Point Theory Appl., 2012:35, 2012] and Latif et al. [Fixed point results for generalized (α,ψ)‐Meir–Keeler contractive mappings and applications, J. Inequal. Appl., 2014:68, 2014]. Some examples and an application are given to support the usability of the obtained results.