Strong Convergence of New Two-Step Viscosity Iterative Approximation Methods for Set-Valued Nonexpansive Mappings in CAT(0) Spaces
This paper is for the purpose of introducing and studying a class of new two-step viscosity iteration approximation methods for finding fixed points of set-valued nonexpansive mappings in CAT(0) spaces. By means of some properties and characteristic to CAT(0) space and using Cauchy-Schwarz inequalit...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/1280241 |
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| _version_ | 1832564625280860160 |
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| author | Ting-jian Xiong Heng-you Lan |
| author_facet | Ting-jian Xiong Heng-you Lan |
| author_sort | Ting-jian Xiong |
| collection | DOAJ |
| description | This paper is for the purpose of introducing and studying a class of new two-step viscosity iteration approximation methods for finding fixed points of set-valued nonexpansive mappings in CAT(0) spaces. By means of some properties and characteristic to CAT(0) space and using Cauchy-Schwarz inequality and Xu’s inequality, strong convergence theorems of the new two-step viscosity iterative process for set-valued nonexpansive and contraction operators in complete CAT(0) spaces are provided. The results of this paper improve and extend the corresponding main theorems in the literature. |
| format | Article |
| id | doaj-art-a7d58e7d09ad433b88d02b4ce23c902f |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a7d58e7d09ad433b88d02b4ce23c902f2025-02-03T01:10:32ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/12802411280241Strong Convergence of New Two-Step Viscosity Iterative Approximation Methods for Set-Valued Nonexpansive Mappings in CAT(0) SpacesTing-jian Xiong0Heng-you Lan1College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong, Sichuan 643000, ChinaCollege of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong, Sichuan 643000, ChinaThis paper is for the purpose of introducing and studying a class of new two-step viscosity iteration approximation methods for finding fixed points of set-valued nonexpansive mappings in CAT(0) spaces. By means of some properties and characteristic to CAT(0) space and using Cauchy-Schwarz inequality and Xu’s inequality, strong convergence theorems of the new two-step viscosity iterative process for set-valued nonexpansive and contraction operators in complete CAT(0) spaces are provided. The results of this paper improve and extend the corresponding main theorems in the literature.http://dx.doi.org/10.1155/2018/1280241 |
| spellingShingle | Ting-jian Xiong Heng-you Lan Strong Convergence of New Two-Step Viscosity Iterative Approximation Methods for Set-Valued Nonexpansive Mappings in CAT(0) Spaces Journal of Function Spaces |
| title | Strong Convergence of New Two-Step Viscosity Iterative Approximation Methods for Set-Valued Nonexpansive Mappings in CAT(0) Spaces |
| title_full | Strong Convergence of New Two-Step Viscosity Iterative Approximation Methods for Set-Valued Nonexpansive Mappings in CAT(0) Spaces |
| title_fullStr | Strong Convergence of New Two-Step Viscosity Iterative Approximation Methods for Set-Valued Nonexpansive Mappings in CAT(0) Spaces |
| title_full_unstemmed | Strong Convergence of New Two-Step Viscosity Iterative Approximation Methods for Set-Valued Nonexpansive Mappings in CAT(0) Spaces |
| title_short | Strong Convergence of New Two-Step Viscosity Iterative Approximation Methods for Set-Valued Nonexpansive Mappings in CAT(0) Spaces |
| title_sort | strong convergence of new two step viscosity iterative approximation methods for set valued nonexpansive mappings in cat 0 spaces |
| url | http://dx.doi.org/10.1155/2018/1280241 |
| work_keys_str_mv | AT tingjianxiong strongconvergenceofnewtwostepviscosityiterativeapproximationmethodsforsetvaluednonexpansivemappingsincat0spaces AT hengyoulan strongconvergenceofnewtwostepviscosityiterativeapproximationmethodsforsetvaluednonexpansivemappingsincat0spaces |