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Strong convergence theorems obtained by a generalized projections hybrid method for families of mappings in Banach spaces |
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| Authors: | Shin-ya Matsushita Wataru Takahashi |
| Institution: | a Department of Electronics and Information Systems, Faculty of Systems Sciences and Technology, Akita Prefectural University, 84-4 Ebinokuchi Tsuchiya, Yurihonjo, Akita, 015-0055, Japan b Faculty of Engineering, Tamagawa University, Tamagawa-Gakuen, Machida-shi, Tokyo, 194-8610, Japan c Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo, 152-8552, Japan |
| Abstract: | Let C be a nonempty, closed and convex subset of a uniformly convex and smooth Banach space and let {Tn} be a family of mappings of C into itself such that the set of all common fixed points of {Tn} is nonempty. We consider a sequence {xn} generated by the hybrid method by generalized projection in mathematical programming. We give conditions on {Tn} under which {xn} converges strongly to a common fixed point of {Tn} and generalize the results given in 12], 14], 13] and 11]. |
| Keywords: | 49M05 47H05 90C25 |
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