Summary: Let

$C$ be a nonempty closed convex subset of a uniformly convex Banach space

$E$ whose norm is Gâteaux differentiable 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 in mathematical programming, and present conditions on

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

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

$\left\{{T}_{n}\right\}$, generalizing the results of [

*K. Nakajo*,

*K. Shimoji* and

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

Zbl 1109.47060);

*S. Ohsawa* and

*W. Takahashi*, Arch. Math. 81, No. 4, 439–445 (2003;

Zbl 1067.47080)].