Approximating fixed points of nonexpansive and generalized nonexpansive mappings
In this paper we consider a mapping S of the form S=α0I+α1T+α2T2+…+αKTK, where αi≥0. α1>0 with ∑i=0kαi=1, and show that in a uniformly convex Banach space the Picard iterates of S converge to a fixed point of T when T is nonexpansive or generalized nonexpansive or even quasinonexpansive....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000092 |
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| _version_ | 1850231118749499392 |
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| author | M. Maiti B. Saha |
| author_facet | M. Maiti B. Saha |
| author_sort | M. Maiti |
| collection | DOAJ |
| description | In this paper we consider a mapping S of the form
S=α0I+α1T+α2T2+…+αKTK,
where αi≥0. α1>0 with ∑i=0kαi=1, and show that in a uniformly convex Banach space the Picard iterates
of S converge to a fixed point of T when T is nonexpansive or generalized nonexpansive or even quasinonexpansive. |
| format | Article |
| id | doaj-art-00fa1b3c6ea1441fad327c8138a2d24f |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-00fa1b3c6ea1441fad327c8138a2d24f2025-08-20T02:03:39ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-01161818610.1155/S0161171293000092Approximating fixed points of nonexpansive and generalized nonexpansive mappingsM. Maiti0B. Saha1Department of Mathematics, Indian Institute of Technology, Kharagpur, IndiaDepartment of Mathematics, Indian Institute of Technology, Kharagpur, IndiaIn this paper we consider a mapping S of the form S=α0I+α1T+α2T2+…+αKTK, where αi≥0. α1>0 with ∑i=0kαi=1, and show that in a uniformly convex Banach space the Picard iterates of S converge to a fixed point of T when T is nonexpansive or generalized nonexpansive or even quasinonexpansive.http://dx.doi.org/10.1155/S0161171293000092fixed pointsnonexpansive mappingsuniformly convex Banach spaces. |
| spellingShingle | M. Maiti B. Saha Approximating fixed points of nonexpansive and generalized nonexpansive mappings International Journal of Mathematics and Mathematical Sciences fixed points nonexpansive mappings uniformly convex Banach spaces. |
| title | Approximating fixed points of nonexpansive and generalized nonexpansive mappings |
| title_full | Approximating fixed points of nonexpansive and generalized nonexpansive mappings |
| title_fullStr | Approximating fixed points of nonexpansive and generalized nonexpansive mappings |
| title_full_unstemmed | Approximating fixed points of nonexpansive and generalized nonexpansive mappings |
| title_short | Approximating fixed points of nonexpansive and generalized nonexpansive mappings |
| title_sort | approximating fixed points of nonexpansive and generalized nonexpansive mappings |
| topic | fixed points nonexpansive mappings uniformly convex Banach spaces. |
| url | http://dx.doi.org/10.1155/S0161171293000092 |
| work_keys_str_mv | AT mmaiti approximatingfixedpointsofnonexpansiveandgeneralizednonexpansivemappings AT bsaha approximatingfixedpointsofnonexpansiveandgeneralizednonexpansivemappings |