In [J. Math. Anal. Appl. 279, No. 2, 372–379 (2003; Zbl 1035.47048
)], K. Nakajo
and W. Takahashi
defined a modified Mann iteration for a single nonexpansive map
to obtain strong convergence results in Hilbert space. In [Nonlinear Anal., Theory Methods Appl. 64, No. 11 (A), 2400–2411 (2006; Zbl 1105.47060
)], C. Martinez–Yanes
and H. K. Xu
defined modified Ishikawa and Halpern iterations to prove interesting convergence results. In the paper under review, the authors, guided by the first mentioned article, prove strong convergence theorems for relatively nonexpansive mappings in uniformly convex and uniformly smooth Banach space.