Some new cyclic admissibility type with uni-dimensional and multidimensional fixed point theorems and its applications

Volume 11, Issue 9, pp 1056--1069 Publication Date: June 19, 2018       Article History


Chirasak Mongkolkeha - Department of Mathematics, Statistics and Computer Sciences, Faculty of Liberal Arts and Science, Kasetsart University, Kamphaeng-Saen Campus, Nakhonpathom 73140, Thailand. Wutiphol Sintunavarat - Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand.


In this paper, we introduce the concept of a cyclic \((\alpha,\beta)\)-admissible mapping type \(S\) and the notion of an \((\alpha,\beta)$-$(\psi,\varphi)\)-contraction type \(S\). We also establish fixed point results for such contractions along with the cyclic \((\alpha,\beta)\)-admissibility type \(S\) in complete \(b\)-metric spaces and provide some examples for supporting our result. Applying our new results, we obtain fixed point results for cyclic mappings and multidimensional fixed point results. As application, the existence of a solution of the nonlinear integral equation is discussed.