The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces
We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of the Mann iteration method and the Ish...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/69542 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832547489729740800 |
|---|---|
| author | Zeqing Liu Li Wang Jeong Sheok Ume Shin Min Kang |
| author_facet | Zeqing Liu Li Wang Jeong Sheok Ume Shin Min Kang |
| author_sort | Zeqing Liu |
| collection | DOAJ |
| description | We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of the Mann iteration method and the Ishikawa iteration method for φ-pseudocontractive operators in nonempty closed convex subsets of uniformly smooth Banach spaces. The results presented in this paper extend and improve the corresponding results in the literature. |
| format | Article |
| id | doaj-art-25707af02fd243e6b31c8f84b3051d28 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-25707af02fd243e6b31c8f84b3051d282025-02-03T06:44:24ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/6954269542The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spacesZeqing Liu0Li Wang1Jeong Sheok Ume2Shin Min Kang3Department of Mathematics, Liaoning Normal University Dalian, Liaoning 116029, ChinaDepartment of Science, Shenyang Institute of Aeronautical Engineering Shenyang, Liaoning 110034, ChinaDepartment of Applied Mathematics, Changwon National University, Changwon 641-773, KoreaDepartment of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Chinju 660-701, KoreaWe investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of the Mann iteration method and the Ishikawa iteration method for φ-pseudocontractive operators in nonempty closed convex subsets of uniformly smooth Banach spaces. The results presented in this paper extend and improve the corresponding results in the literature.http://dx.doi.org/10.1155/IJMMS/2006/69542 |
| spellingShingle | Zeqing Liu Li Wang Jeong Sheok Ume Shin Min Kang The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces International Journal of Mathematics and Mathematical Sciences |
| title | The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces |
| title_full | The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces |
| title_fullStr | The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces |
| title_full_unstemmed | The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces |
| title_short | The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces |
| title_sort | equivalence between the convergences of mann and ishikawa iteration methods with errors for demicontinuous φ strongly accretive operators in uniformly smooth banach spaces |
| url | http://dx.doi.org/10.1155/IJMMS/2006/69542 |
| work_keys_str_mv | AT zeqingliu theequivalencebetweentheconvergencesofmannandishikawaiterationmethodswitherrorsfordemicontinuousphstronglyaccretiveoperatorsinuniformlysmoothbanachspaces AT liwang theequivalencebetweentheconvergencesofmannandishikawaiterationmethodswitherrorsfordemicontinuousphstronglyaccretiveoperatorsinuniformlysmoothbanachspaces AT jeongsheokume theequivalencebetweentheconvergencesofmannandishikawaiterationmethodswitherrorsfordemicontinuousphstronglyaccretiveoperatorsinuniformlysmoothbanachspaces AT shinminkang theequivalencebetweentheconvergencesofmannandishikawaiterationmethodswitherrorsfordemicontinuousphstronglyaccretiveoperatorsinuniformlysmoothbanachspaces AT zeqingliu equivalencebetweentheconvergencesofmannandishikawaiterationmethodswitherrorsfordemicontinuousphstronglyaccretiveoperatorsinuniformlysmoothbanachspaces AT liwang equivalencebetweentheconvergencesofmannandishikawaiterationmethodswitherrorsfordemicontinuousphstronglyaccretiveoperatorsinuniformlysmoothbanachspaces AT jeongsheokume equivalencebetweentheconvergencesofmannandishikawaiterationmethodswitherrorsfordemicontinuousphstronglyaccretiveoperatorsinuniformlysmoothbanachspaces AT shinminkang equivalencebetweentheconvergencesofmannandishikawaiterationmethodswitherrorsfordemicontinuousphstronglyaccretiveoperatorsinuniformlysmoothbanachspaces |