Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert Spaces
Viscosity approximation methods for nonexpansive nonself-mappings are studied. Let C be a nonempty closed convex subset of Hilbert space H, P a metric projection of H onto C and let T be a nonexpansive nonself-mapping from C into H. For a contraction f on C and {tn}⊆(0,1), let xn be the unique fixe...
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2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/48648 |
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| author | Rabian Wangkeeree |
| author_facet | Rabian Wangkeeree |
| author_sort | Rabian Wangkeeree |
| collection | DOAJ |
| description | Viscosity approximation methods for nonexpansive nonself-mappings are studied.
Let C be a nonempty closed convex subset of Hilbert space H, P a metric projection of H onto C and let T be a nonexpansive nonself-mapping from C into H. For a contraction f on C and {tn}⊆(0,1), let xn be the unique fixed point of the contraction x↦tnf(x)+(1−tn)(1/n)∑j=1n(PT)jx. Consider also the iterative processes
{yn} and {zn} generated by yn+1=αnf(yn)+(1−αn)(1/(n+1))∑j=0n(PT)jyn, n≥0, and zn+1=(1/(n+1))∑j=0nP(αnf(zn)+(1−αn)(TP)jzn),n≥0, where y0,z0∈C,{αn} is a real sequence in an interval [0,1]. Strong convergence of the sequences {xn},{yn}, and {zn} to a fixed point of T which solves some variational inequalities is obtained under certain appropriate conditions on the real sequences {αn} and {tn}. |
| format | Article |
| id | doaj-art-12ab7378c9194e17a241fe52c1affcfc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-12ab7378c9194e17a241fe52c1affcfc2025-02-03T01:07:00ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/4864848648Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert SpacesRabian Wangkeeree0Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandViscosity approximation methods for nonexpansive nonself-mappings are studied. Let C be a nonempty closed convex subset of Hilbert space H, P a metric projection of H onto C and let T be a nonexpansive nonself-mapping from C into H. For a contraction f on C and {tn}⊆(0,1), let xn be the unique fixed point of the contraction x↦tnf(x)+(1−tn)(1/n)∑j=1n(PT)jx. Consider also the iterative processes {yn} and {zn} generated by yn+1=αnf(yn)+(1−αn)(1/(n+1))∑j=0n(PT)jyn, n≥0, and zn+1=(1/(n+1))∑j=0nP(αnf(zn)+(1−αn)(TP)jzn),n≥0, where y0,z0∈C,{αn} is a real sequence in an interval [0,1]. Strong convergence of the sequences {xn},{yn}, and {zn} to a fixed point of T which solves some variational inequalities is obtained under certain appropriate conditions on the real sequences {αn} and {tn}.http://dx.doi.org/10.1155/2007/48648 |
| spellingShingle | Rabian Wangkeeree Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert Spaces International Journal of Mathematics and Mathematical Sciences |
| title | Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert
Spaces |
| title_full | Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert
Spaces |
| title_fullStr | Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert
Spaces |
| title_full_unstemmed | Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert
Spaces |
| title_short | Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert
Spaces |
| title_sort | viscosity approximation methods for nonexpansive nonself mappings in hilbert spaces |
| url | http://dx.doi.org/10.1155/2007/48648 |
| work_keys_str_mv | AT rabianwangkeeree viscosityapproximationmethodsfornonexpansivenonselfmappingsinhilbertspaces |