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Title: | An iterative method with residual vectors for solving the fixed point and the split inclusion problems in Banach spaces |
Authors: | Prasit Cholamjiak Suthep Suantai Pongsakorn Sunthrayuth |
Authors: | Prasit Cholamjiak Suthep Suantai Pongsakorn Sunthrayuth |
Keywords: | Mathematics |
Issue Date: | 1-Mar-2019 |
Abstract: | © 2019, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional. In this paper, we propose an iterative technique with residual vectors for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of a split inclusion problem (SIP) with a way of selecting the stepsizes without prior knowledge of the operator norm in the framework of p-uniformly convex and uniformly smooth Banach spaces. Then strong convergence of the proposed algorithm to a common element of the above two sets is proved. As applications, we apply our result to find the set of common fixed points of a family of mappings which is also a solution of the SIP. We also give a numerical example and demonstrate the efficiency of the proposed algorithm. The results presented in this paper improve and generalize many recent important results in the literature. |
URI: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85060925947&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/63682 |
ISSN: | 18070302 01018205 |
Appears in Collections: | CMUL: Journal Articles |
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