Summary: Let

$C$ be a nonempty, closed and convex subset of a uniformly convex and smooth Banach space and let

$\left\{{T}_{n}\right\}$ be a family of mappings of

$C$ into itself such that the set of all common fixed points of

$\left\{{T}_{n}\right\}$ is nonempty. We consider a sequence

$\left\{{x}_{n}\right\}$ generated by the hybrid method by generalized projection in mathematical programming. We give conditions on

$\left\{{T}_{n}\right\}$ under which

$\left\{{x}_{n}\right\}$ converges strongly to a common fixed point of

$\left\{{T}_{n}\right\}$ and generalize the results given in [

*S. Kamimura* and

*W. Takahashi*, SIAM J. Optim. 13, No. 3, 938–945 (2003;

Zbl 1101.90083);

*F. Kohsaka* and

*W. Takahashi*, J. Nonlinear Convex Anal. 5, No. 3, 407–414 (2004;

Zbl 1071.47062);

*S.-y. Matsushita* and

*W. Takahashi*, Approximation Theory 134, No. 2, 257–266 (2005;

Zbl 1071.47063);

*K. Nakajo, J, Shimoji* and

*W. Takahashi*, Taiwanese J. Math. 10, No. 2, 339–360 (2006;

Zbl 1109.47060)].