Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces

By S. Matsushita, Wataru Takahashi. 2004

169 citations recorded by the source corpus.

We first introduce an iterative sequence for finding fixed points of relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by using the notion of generalized projection. We apply these results to the convex feasibility problem and a proximal-type algorithm for monotone operators in Banach spaces.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/752c6e3f02c5db0a5c9d55e27142a3d099de40ed

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In Computational Theory and Mathematics

In Geometry and Topology

In Numerical Analysis

Citations in the corpus

Parallel Hybrid Iterative Methods for Variational Inequalities, Equilibrium Problems, and Common Fixed Point Problems (2015, methodology): “Takahashi and Toyoda [19] proposed a weakly convergent method for finding P. K. Anh (Corresponding author) · D.V. Hieu College of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam E-mail: anhpk@vnu.edu.vn, dv.hieu83@gmail.com a common element of the set of fixe”
A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces (2010, background): “In 2004, Matsushita and Takahashi [40] introduced the following iteration sequence {xn}: xn+1 = ΠC J(αnJxn + (1− αn)JTxn) (1.”
Fixed Point Theorems and Ergodic Theorems for Nonlinear Mappings in Hilbert Spaces (2011, unknown): “Using Lemma 6.1 and the technique developed by [14, 27 ], we prove the following theorem.”
Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces (2008, background): “After that, we prove that every nonspreading mapping in a Banach space with a fixed point is relatively nonexpansive in the sense of Matsushita and Takahashi [ 21 , 22] (Theorem 3.3).”