Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces
In this paper, we propose the generalized M-iteration process for approximating the fixed points from Banach spaces to hyperbolic spaces. Using our new iteration process, we prove Δ-convergence and strong convergence theorems for the class of mappings satisfying the condition Cλ and the condition E...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2020/6435043 |
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| author | Preeyalak Chuadchawna Ali Farajzadeh Anchalee Kaewcharoen |
| author_facet | Preeyalak Chuadchawna Ali Farajzadeh Anchalee Kaewcharoen |
| author_sort | Preeyalak Chuadchawna |
| collection | DOAJ |
| description | In this paper, we propose the generalized M-iteration process for approximating the fixed points from Banach spaces to hyperbolic spaces. Using our new iteration process, we prove Δ-convergence and strong convergence theorems for the class of mappings satisfying the condition Cλ and the condition E which is the generalization of Suzuki generalized nonexpansive mappings in the setting of hyperbolic spaces. Moreover, a numerical example is given to present the capability of our iteration process and the solution of the integral equation is also illustrated using our main result. |
| format | Article |
| id | doaj-art-c8712432e22f4fde8d317cda934254a3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c8712432e22f4fde8d317cda934254a32025-02-03T06:46:37ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/64350436435043Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic SpacesPreeyalak Chuadchawna0Ali Farajzadeh1Anchalee Kaewcharoen2Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, Razi University, Kermanshah 67149, IranDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandIn this paper, we propose the generalized M-iteration process for approximating the fixed points from Banach spaces to hyperbolic spaces. Using our new iteration process, we prove Δ-convergence and strong convergence theorems for the class of mappings satisfying the condition Cλ and the condition E which is the generalization of Suzuki generalized nonexpansive mappings in the setting of hyperbolic spaces. Moreover, a numerical example is given to present the capability of our iteration process and the solution of the integral equation is also illustrated using our main result.http://dx.doi.org/10.1155/2020/6435043 |
| spellingShingle | Preeyalak Chuadchawna Ali Farajzadeh Anchalee Kaewcharoen Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces International Journal of Mathematics and Mathematical Sciences |
| title | Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces |
| title_full | Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces |
| title_fullStr | Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces |
| title_full_unstemmed | Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces |
| title_short | Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces |
| title_sort | fixed point approximations of generalized nonexpansive mappings via generalized m iteration process in hyperbolic spaces |
| url | http://dx.doi.org/10.1155/2020/6435043 |
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