Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point Problem
In this article, we study the extended split equality problem and extended split equality fixed point problem, which are extensions of the convex feasibility problem. For solving the extended split equality problem, we present two self-adaptive stepsize algorithms with internal perturbation projecti...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/6034754 |
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| _version_ | 1832567778639347712 |
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| author | Meixia Li Xueling Zhou Wenchao Wang |
| author_facet | Meixia Li Xueling Zhou Wenchao Wang |
| author_sort | Meixia Li |
| collection | DOAJ |
| description | In this article, we study the extended split equality problem and extended split equality fixed point problem, which are extensions of the convex feasibility problem. For solving the extended split equality problem, we present two self-adaptive stepsize algorithms with internal perturbation projection and obtain the weak and the strong convergence of the algorithms, respectively. Furthermore, based on the operators being quasinonexpansive, we offer an iterative algorithm to solve the extended split equality fixed point problem. We introduce a way of selecting the stepsize which does not need any prior information about operator norms in the three algorithms. We apply our iterative algorithms to some convex and nonlinear problems. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithms. |
| format | Article |
| id | doaj-art-18101d25f7ab47918dee52c4a6e3751d |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-18101d25f7ab47918dee52c4a6e3751d2025-02-03T01:00:30ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/60347546034754Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point ProblemMeixia Li0Xueling Zhou1Wenchao Wang2School of Mathematics and Information Science, Weifang University, Weifang Shandong 261061, ChinaCollege of Mathematics and System Science, Shandong University of Science and Technology, Qingdao Shandong 266590, ChinaCollege of Mathematics and System Science, Shandong University of Science and Technology, Qingdao Shandong 266590, ChinaIn this article, we study the extended split equality problem and extended split equality fixed point problem, which are extensions of the convex feasibility problem. For solving the extended split equality problem, we present two self-adaptive stepsize algorithms with internal perturbation projection and obtain the weak and the strong convergence of the algorithms, respectively. Furthermore, based on the operators being quasinonexpansive, we offer an iterative algorithm to solve the extended split equality fixed point problem. We introduce a way of selecting the stepsize which does not need any prior information about operator norms in the three algorithms. We apply our iterative algorithms to some convex and nonlinear problems. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithms.http://dx.doi.org/10.1155/2020/6034754 |
| spellingShingle | Meixia Li Xueling Zhou Wenchao Wang Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point Problem Journal of Function Spaces |
| title | Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point Problem |
| title_full | Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point Problem |
| title_fullStr | Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point Problem |
| title_full_unstemmed | Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point Problem |
| title_short | Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point Problem |
| title_sort | internal perturbation projection algorithm for the extended split equality problem and the extended split equality fixed point problem |
| url | http://dx.doi.org/10.1155/2020/6034754 |
| work_keys_str_mv | AT meixiali internalperturbationprojectionalgorithmfortheextendedsplitequalityproblemandtheextendedsplitequalityfixedpointproblem AT xuelingzhou internalperturbationprojectionalgorithmfortheextendedsplitequalityproblemandtheextendedsplitequalityfixedpointproblem AT wenchaowang internalperturbationprojectionalgorithmfortheextendedsplitequalityproblemandtheextendedsplitequalityfixedpointproblem |