The Equivalence of Convergence Results of Modified Mann and Ishikawa Iterations with Errors without Bounded Range Assumption
Let E be an arbitrary uniformly smooth real Banach space, let D be a nonempty closed convex subset of E, and let T:D→D be a uniformly generalized Lipschitz generalized asymptotically Φ-strongly pseudocontractive mapping with q∈F(T)≠∅. Let {an},{bn},{cn},{dn} be four real sequences in [0,1] and satis...
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/909187 |
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| author | Zhiqun Xue Yaning Wang Haiyun Zhou |
| author_facet | Zhiqun Xue Yaning Wang Haiyun Zhou |
| author_sort | Zhiqun Xue |
| collection | DOAJ |
| description | Let E be an arbitrary uniformly smooth real Banach space, let D be a nonempty closed convex subset of E, and let T:D→D be a uniformly generalized Lipschitz generalized asymptotically Φ-strongly pseudocontractive mapping with q∈F(T)≠∅. Let {an},{bn},{cn},{dn} be four real sequences in [0,1] and satisfy the conditions: (i) an+cn≤1, bn+dn≤1; (ii) an,bn,dn→0 as n→∞ and cn=o(an); (iii) Σn=0∞an=∞. For some x0,z0∈D, let {un},{vn},{wn} be any bounded sequences in D, and let {xn},{zn} be the modified Ishikawa and Mann iterative sequences with errors, respectively. Then the convergence of {xn} is equivalent to that of {zn}. |
| format | Article |
| id | doaj-art-f3724bcf579c450d9aa23aae929e4877 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f3724bcf579c450d9aa23aae929e48772025-02-03T01:23:32ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/909187909187The Equivalence of Convergence Results of Modified Mann and Ishikawa Iterations with Errors without Bounded Range AssumptionZhiqun Xue0Yaning Wang1Haiyun Zhou2Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, ChinaDepartment of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, ChinaDepartment of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaLet E be an arbitrary uniformly smooth real Banach space, let D be a nonempty closed convex subset of E, and let T:D→D be a uniformly generalized Lipschitz generalized asymptotically Φ-strongly pseudocontractive mapping with q∈F(T)≠∅. Let {an},{bn},{cn},{dn} be four real sequences in [0,1] and satisfy the conditions: (i) an+cn≤1, bn+dn≤1; (ii) an,bn,dn→0 as n→∞ and cn=o(an); (iii) Σn=0∞an=∞. For some x0,z0∈D, let {un},{vn},{wn} be any bounded sequences in D, and let {xn},{zn} be the modified Ishikawa and Mann iterative sequences with errors, respectively. Then the convergence of {xn} is equivalent to that of {zn}.http://dx.doi.org/10.1155/2012/909187 |
| spellingShingle | Zhiqun Xue Yaning Wang Haiyun Zhou The Equivalence of Convergence Results of Modified Mann and Ishikawa Iterations with Errors without Bounded Range Assumption Abstract and Applied Analysis |
| title | The Equivalence of Convergence Results of Modified Mann and Ishikawa Iterations with Errors without Bounded Range Assumption |
| title_full | The Equivalence of Convergence Results of Modified Mann and Ishikawa Iterations with Errors without Bounded Range Assumption |
| title_fullStr | The Equivalence of Convergence Results of Modified Mann and Ishikawa Iterations with Errors without Bounded Range Assumption |
| title_full_unstemmed | The Equivalence of Convergence Results of Modified Mann and Ishikawa Iterations with Errors without Bounded Range Assumption |
| title_short | The Equivalence of Convergence Results of Modified Mann and Ishikawa Iterations with Errors without Bounded Range Assumption |
| title_sort | equivalence of convergence results of modified mann and ishikawa iterations with errors without bounded range assumption |
| url | http://dx.doi.org/10.1155/2012/909187 |
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