Approximating fixed points of some mappings
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- by Ramendra Krishna Bose and Rathindra Nath Mukherjee PDF
- Proc. Amer. Math. Soc. 82 (1981), 603-606 Request permission
Abstract:
In a uniformly convex Banach space, Senter and Dotson, Jr., have given conditions under which certain types of iterates of a quasi-nonexpansive mapping converge to a fixed point of the mapping. Here we consider two types of mappings, one considered by Ray and the other considered by Goebel, Kirk and Shimi, and prove some results concerning the approximations of fixed points of such mappings. A result of Kannan is obtained as a particular case of our result under relaxed conditions.References
- W. G. Dotson Jr., Fixed points of quasi-nonexpansive mappings, J. Austral. Math. Soc. 13 (1972), 167–170. MR 0298499
- K. Goebel, W. A. Kirk, and Tawfik N. Shimi, A fixed point theorem in uniformly convex spaces, Boll. Un. Mat. Ital. (4) 7 (1973), 67–75 (English, with Italian summary). MR 0320834
- R. Kannan, Some results on fixed points. III, Fund. Math. 70 (1971), no. 2, 169–177. MR 283649, DOI 10.4064/fm-70-2-169-177
- W. Robert Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506–510. MR 54846, DOI 10.1090/S0002-9939-1953-0054846-3
- Barada K. Ray, A fixed point theorem in Banach space, Indian J. Pure Appl. Math. 8 (1977), no. 8, 903–907. MR 482411
- H. F. Senter and W. G. Dotson Jr., Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974), 375–380. MR 346608, DOI 10.1090/S0002-9939-1974-0346608-8
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 603-606
- MSC: Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-1981-0614886-7
- MathSciNet review: 614886