Abstract
Let
C
be a nonempty closed convex subset of a uniformly convex Banach space
E
whose norm is Gâteaux differentiable and let
{
T
n
}
be a family of mappings of
C
into itself such that the set of all common fixed points of
{
T
n
}
is nonempty. We consider a sequence
{
x
n
}
generated by the hybrid method in mathematical programming. And we give the conditions of
{
T
n
}
under which
{
x
n
}
converges strongly to a common fixed point of
{
T
n
}
and generalize the results of [K. Nakajo, K. Shimoji, W. Takahashi, Strong convergence theorems by the hybrid method for families of nonexpansive mappings in Hilbert spaces, Taiwanese J. Math. 10 (2006) 339–360; S. Ohsawa, W. Takahashi, Strong convergence theorems for resolvents of maximal monotone operators in Banach spaces, Arch. Math. 81 (2003) 439–445].