Strong Convergence for Hybrid Implicit S-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings
Let K be a nonempty closed convex subset of a real Banach space E, let S:K→K be nonexpansive, and let T:K→K be Lipschitz strongly pseudocontractive mappings such that p∈FS∩FT=x∈K:Sx=Tx=x and x-Sy≤Sx-Sy and x-Ty≤Tx-Ty for all x, y∈K. Let βn be a sequence in 0, 1 satisfying (i) ∑n=1∞βn=∞; (ii) limn→∞...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/735673 |
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| author | Shin Min Kang Arif Rafiq Faisal Ali Young Chel Kwun |
| author_facet | Shin Min Kang Arif Rafiq Faisal Ali Young Chel Kwun |
| author_sort | Shin Min Kang |
| collection | DOAJ |
| description | Let K be a nonempty closed convex subset of a real Banach space E, let S:K→K be nonexpansive, and let T:K→K be Lipschitz strongly pseudocontractive mappings such that p∈FS∩FT=x∈K:Sx=Tx=x and x-Sy≤Sx-Sy and x-Ty≤Tx-Ty for all x, y∈K. Let βn be a sequence in 0, 1 satisfying (i) ∑n=1∞βn=∞; (ii) limn→∞βn=0. For arbitrary x0∈K, let xn be a sequence iteratively defined by xn=Syn, yn=1-βnxn-1+βnTxn, n≥1. Then the sequence xn converges strongly to a common fixed point p of S and T. |
| format | Article |
| id | doaj-art-07860b723c124b86a83078024500f411 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-07860b723c124b86a83078024500f4112025-02-03T06:14:11ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/735673735673Strong Convergence for Hybrid Implicit S-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive MappingsShin Min Kang0Arif Rafiq1Faisal Ali2Young Chel Kwun3Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of KoreaDepartment of Mathematics, Lahore Leads University, Lahore 54810, PakistanCentre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, PakistanDepartment of Mathematics, Dong-A University, Busan 604-714, Republic of KoreaLet K be a nonempty closed convex subset of a real Banach space E, let S:K→K be nonexpansive, and let T:K→K be Lipschitz strongly pseudocontractive mappings such that p∈FS∩FT=x∈K:Sx=Tx=x and x-Sy≤Sx-Sy and x-Ty≤Tx-Ty for all x, y∈K. Let βn be a sequence in 0, 1 satisfying (i) ∑n=1∞βn=∞; (ii) limn→∞βn=0. For arbitrary x0∈K, let xn be a sequence iteratively defined by xn=Syn, yn=1-βnxn-1+βnTxn, n≥1. Then the sequence xn converges strongly to a common fixed point p of S and T.http://dx.doi.org/10.1155/2014/735673 |
| spellingShingle | Shin Min Kang Arif Rafiq Faisal Ali Young Chel Kwun Strong Convergence for Hybrid Implicit S-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings Abstract and Applied Analysis |
| title | Strong Convergence for Hybrid Implicit S-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings |
| title_full | Strong Convergence for Hybrid Implicit S-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings |
| title_fullStr | Strong Convergence for Hybrid Implicit S-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings |
| title_full_unstemmed | Strong Convergence for Hybrid Implicit S-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings |
| title_short | Strong Convergence for Hybrid Implicit S-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings |
| title_sort | strong convergence for hybrid implicit s iteration scheme of nonexpansive and strongly pseudocontractive mappings |
| url | http://dx.doi.org/10.1155/2014/735673 |
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