An iterative method with residual vectors for solving the fixed point and the split inclusion problems in Banach spaces

• Main Authors: Prasit Cholamjiak, Suthep Suantai, Pongsakorn Sunthrayuth
• Format: Journal
• Published: 2019
• Subjects: Mathematics
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85060925947&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/63682
• Institution: Chiang Mai University

© 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.