## Strong convergence theorems of a new hybrid projection method for finite family of two hemi-relatively nonexpansive mappings in a Banach space

### Volume 92 / 2011

Banach Center Publications 92 (2011), 379-390
MSC: Primary 47H10; Secondary 47H09.
DOI: 10.4064/bc92-0-26

#### Abstract

In this paper, we prove strong convergence theorems of the hybrid
projection algorithms for finite family of two hemi-relatively
nonexpansive mappings in a Banach space. Using this result, we
also discuss the resolvents of two maximal monotone operators in a
Banach space. Our results modify and improve the recently ones
announced by Plubtieng and Ungchittrakool [*Strong convergence
theorems for a common fixed point of two relatively nonexpansive
mappings in a Banach space*, J. Approx. Theory
149 (2007), 103–115], Matsushita and Takahashi [*A strong
convergence theorem for relatively nonexpansive mappings in a
Banach space*, J. Approx. Theory 134 (2005),
257–266] and many others.