Implicit iteration process of nonexpansive non-self-mappings
Suppose C is a nonempty closed convex subset of real Hilbert space H. Let T:C→H be a nonexpansive non-self-mapping and P is the nearest point projection of H onto C. In this paper, we study the convergence of the sequences {xn}, {yn}, {zn} satisfying xn=(1−αn)u+αnT[(1−βn)xn+βnTxn], yn=(1−αn)u+αnPT[(...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3103 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832551525341200384 |
|---|---|
| author | Somyot Plubtieng Rattanaporn Punpaeng |
| author_facet | Somyot Plubtieng Rattanaporn Punpaeng |
| author_sort | Somyot Plubtieng |
| collection | DOAJ |
| description | Suppose C is a nonempty closed convex subset of real Hilbert space H. Let T:C→H be a nonexpansive non-self-mapping and P is the nearest point projection of H onto C. In this paper, we study the convergence of the sequences {xn}, {yn}, {zn} satisfying xn=(1−αn)u+αnT[(1−βn)xn+βnTxn], yn=(1−αn)u+αnPT[(1−βn)yn+βnPTyn], and zn=P[(1−αn)u+αnTP[(1−βn)zn+βnTzn]], where {αn}⊆(0,1), 0≤βn≤β<1 and αn→1 as n→∞. Our results extend and improve the recent ones announced by Xu and Yin, and many others. |
| format | Article |
| id | doaj-art-38d12c96be79487f968b77eab2d8c0ea |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-38d12c96be79487f968b77eab2d8c0ea2025-02-03T06:01:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005193103311010.1155/IJMMS.2005.3103Implicit iteration process of nonexpansive non-self-mappingsSomyot Plubtieng0Rattanaporn Punpaeng1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandSuppose C is a nonempty closed convex subset of real Hilbert space H. Let T:C→H be a nonexpansive non-self-mapping and P is the nearest point projection of H onto C. In this paper, we study the convergence of the sequences {xn}, {yn}, {zn} satisfying xn=(1−αn)u+αnT[(1−βn)xn+βnTxn], yn=(1−αn)u+αnPT[(1−βn)yn+βnPTyn], and zn=P[(1−αn)u+αnTP[(1−βn)zn+βnTzn]], where {αn}⊆(0,1), 0≤βn≤β<1 and αn→1 as n→∞. Our results extend and improve the recent ones announced by Xu and Yin, and many others.http://dx.doi.org/10.1155/IJMMS.2005.3103 |
| spellingShingle | Somyot Plubtieng Rattanaporn Punpaeng Implicit iteration process of nonexpansive non-self-mappings International Journal of Mathematics and Mathematical Sciences |
| title | Implicit iteration process of nonexpansive non-self-mappings |
| title_full | Implicit iteration process of nonexpansive non-self-mappings |
| title_fullStr | Implicit iteration process of nonexpansive non-self-mappings |
| title_full_unstemmed | Implicit iteration process of nonexpansive non-self-mappings |
| title_short | Implicit iteration process of nonexpansive non-self-mappings |
| title_sort | implicit iteration process of nonexpansive non self mappings |
| url | http://dx.doi.org/10.1155/IJMMS.2005.3103 |
| work_keys_str_mv | AT somyotplubtieng implicititerationprocessofnonexpansivenonselfmappings AT rattanapornpunpaeng implicititerationprocessofnonexpansivenonselfmappings |