Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces
We study the widely more generalized hybrid mappings which have been proposed to unify several well-known nonlinear mappings including the nonexpansive mappings, nonspreading mappings, hybrid mappings, and generalized hybrid mappings. Without the convexity assumption, we will establish the existence...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/904164 |
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| author | Sy-Ming Guu Wataru Takahashi |
| author_facet | Sy-Ming Guu Wataru Takahashi |
| author_sort | Sy-Ming Guu |
| collection | DOAJ |
| description | We study the widely more generalized hybrid mappings which have been proposed to unify several well-known nonlinear mappings including the nonexpansive mappings, nonspreading mappings, hybrid
mappings, and generalized hybrid mappings. Without the convexity assumption, we will establish the existence theorem and mean convergence theorem
for attractive point of the widely more generalized hybrid mappings in a Hilbert
space. Moreover, we prove a weak convergence theorem of Mann’s type and a
strong convergence theorem of Shimizu and Takahashi’s type for such a wide
class of nonlinear mappings in a Hilbert space. Our results can be viewed as a
generalization of Kocourek, Takahashi and Yao, and Hojo and Takahashi where
they studied the generalized hybrid mappings. |
| format | Article |
| id | doaj-art-eb454dec36514b18a23b85bd419ea65a |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-eb454dec36514b18a23b85bd419ea65a2025-08-20T02:22:21ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/904164904164Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert SpacesSy-Ming Guu0Wataru Takahashi1Graduate Institute of Business and Management, College of Management, Chang-Gung University, Kwei-Shan, Taoyuan Hsien 330, TaiwanDepartment of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, JapanWe study the widely more generalized hybrid mappings which have been proposed to unify several well-known nonlinear mappings including the nonexpansive mappings, nonspreading mappings, hybrid mappings, and generalized hybrid mappings. Without the convexity assumption, we will establish the existence theorem and mean convergence theorem for attractive point of the widely more generalized hybrid mappings in a Hilbert space. Moreover, we prove a weak convergence theorem of Mann’s type and a strong convergence theorem of Shimizu and Takahashi’s type for such a wide class of nonlinear mappings in a Hilbert space. Our results can be viewed as a generalization of Kocourek, Takahashi and Yao, and Hojo and Takahashi where they studied the generalized hybrid mappings.http://dx.doi.org/10.1155/2013/904164 |
| spellingShingle | Sy-Ming Guu Wataru Takahashi Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces Abstract and Applied Analysis |
| title | Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces |
| title_full | Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces |
| title_fullStr | Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces |
| title_full_unstemmed | Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces |
| title_short | Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces |
| title_sort | existence and approximation of attractive points of the widely more generalized hybrid mappings in hilbert spaces |
| url | http://dx.doi.org/10.1155/2013/904164 |
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