Approximation of fixed points of strictly pseudocontractive mappings on arbitrary closed, convex sets in a Banach space
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- by K. P. R. Sastry and G. V. R. Babu PDF
- Proc. Amer. Math. Soc. 128 (2000), 2907-2909 Request permission
Abstract:
We show that any fixed point of a Lipschitzian, strictly pseudocontractive mapping $T$ on a closed, convex subset $K$ of a Banach space $X$ is necessarily unique, and may be norm approximated by an iterative procedure. Our argument provides a convergence rate estimate and removes the boundedness assumption on $K$, generalizing theorems of Liu.References
- Liwei Liu, Approximation of fixed points of a strictly pseudocontractive mapping, Proc. Amer. Math. Soc. 125 (1997), no. 5, 1363–1366. MR 1430761, DOI 10.1090/S0002-9939-97-03858-6
Additional Information
- K. P. R. Sastry
- Affiliation: Department of Mathematics, Andhra University, Visakhapatnam 530 003, India
- G. V. R. Babu
- Affiliation: Department of Mathematics, Andhra University, Visakhapatnam 530 003, India
- Received by editor(s): May 4, 1998
- Received by editor(s) in revised form: November 2, 1998
- Published electronically: March 2, 2000
- Additional Notes: This research was supported by UGC, India, Grant No. U4/4997/97-98.
- Communicated by: Dale Alspach
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2907-2909
- MSC (1991): Primary 47H17
- DOI: https://doi.org/10.1090/S0002-9939-00-05362-4
- MathSciNet review: 1664363