Geodesic
Some new cyclic admissibility type with uni-dimensional and multidimensional fixed point theorems and its applications
Mongkolkeha, Chirasak 1 ; Sintunavarat, Wutiphol 2
1 Department of Mathematics, Statistics and Computer Sciences, Faculty of Liberal Arts and Science, Kasetsart University, Kamphaeng-Saen Campus, Nakhonpathom 73140, Thailand
2 Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 9, p. 1056-1069.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.011.09.04
Classification : 47H09, 47H10, 54H25
Keywords: \(\alpha\)-admissible mappings, cyclic \((\alpha,\beta)\)-admissible mappings, generalized weak contraction mappings, multidimensional fixed points, nonlinear integral equations

Mongkolkeha, Chirasak  1 ; Sintunavarat, Wutiphol  2

1 Department of Mathematics, Statistics and Computer Sciences, Faculty of Liberal Arts and Science, Kasetsart University, Kamphaeng-Saen Campus, Nakhonpathom 73140, Thailand
2 Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand 
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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 its applications, Tome 11 (2018) no. 9, p. 1056-1069. doi : 10.22436/jnsa.011.09.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.09.04/

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