Weak and Strong Convergence Theorems for Relatively Nonexpansive Mappings in Banach Spaces

@inproceedings{Matsushita2004WeakAS,
title={Weak and Strong Convergence Theorems for Relatively Nonexpansive Mappings in Banach Spaces},
author={Shin-ya Matsushita and Wataru Takahashi},
year={2004}
}

where {rn} ⊂ (0,∞) and Jr = (I + rA)−1 for all r > 0. This algorithm was first introduced by Martinet [9]. In [16], Rockafellar proved that if liminfn→∞ rn > 0 and A−10 = ∅, then the sequence {xn} defined by (1.2) converges weakly to an element of solutions of (1.1). On the other hand, Kamimura and Takahashi [4] considered an algorithm to generate a strong convergent sequence in a Hilbert space. Further, Kamimura and Takahashi’s result was extended to more general Banach spaces by Kohsaka and… CONTINUE READING