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Wataru Takahashi, A weak convergence theorem for relatively nonexpansive mappings and maximal monotone operators in a Banach space

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DOI: 10.23952/jano.3.2021.1.11
Volume 3, Issue 1, 30 April 2021, Pages 197-210

 

Abstract. In this paper, using the idea of Mann’s iteration, we prove a weak convergence theorem for finding a common element of the fixed point sets of two relatively nonexpansive mappings and the zero point set of a maximal monotone operator in a Banach space. We apply this result to get well-known and new weak convergence theorems which are connected with relatively nonexpansive mappings and maximal monotone operators in Hilbert spaces and in Banach spaces.

 

How to Cite this Article:
Wataru Takahashi, A weak convergence theorem for relatively nonexpansive mappings and maximal monotone operators in a Banach space, J. Appl. Numer. Optim. 3 (2021), 197-210.