Summary: We establish strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space by using the hybrid method in mathematical programming. Our results extend and improve the recent ones announced by S.-Y. Matsushita
and W. Takahashi
[J. Approximation Theory 134, No. 2, 257–266 (2005; Zbl 1071.47063
)], C. Martinez-Yanes
and H.-K. Xu
[Nonlinear Anal., Theory Methods Appl. 64, No. 11 (A), 2400–2411 (2006; Zbl 1105.47060
)], and many others.