Some new cyclic admissibility type with uni-dimensional and multidimensional fixed point theorems and its applications
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Authors
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.
Abstract
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.
Share and Cite
ISRP Style
Chirasak Mongkolkeha, Wutiphol Sintunavarat, Some new cyclic admissibility type with uni-dimensional and multidimensional fixed point theorems and its applications, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 9, 1056--1069
AMA Style
Mongkolkeha Chirasak, Sintunavarat Wutiphol, Some new cyclic admissibility type with uni-dimensional and multidimensional fixed point theorems and its applications. J. Nonlinear Sci. Appl. (2018); 11(9):1056--1069
Chicago/Turabian Style
Mongkolkeha, Chirasak, Sintunavarat, Wutiphol. "Some new cyclic admissibility type with uni-dimensional and multidimensional fixed point theorems and its applications." Journal of Nonlinear Sciences and Applications, 11, no. 9 (2018): 1056--1069
Keywords
- \(\alpha\)-admissible mappings
- cyclic \((\alpha,\beta)\)-admissible mappings
- generalized weak contraction mappings
- multidimensional fixed points
- nonlinear integral equations
MSC
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