*(English)*Zbl 1005.47053

The authors present extensions and generalisations of theorems related with approximating fixed points due to *Ya. Alber* and *S. Guerre-Delabriere* [Analysis, München 21, No. 1, 17-39 (2001; Zbl 0985.47044)] from real Hilbert spaces to more general real uniformly smooth Banach spaces. We cite two results briefly stated in the abstract:

Let $K$ be a closed convex subset of a real uniformly smooth Banach space $E\xb7$ Suppose $K$ is a nonexpansive retract of $E$ with $P$ as the nonexpansive retraction. Let $T:K\to E$ be a d-weakly contractive map such that a fixed point ${x}^{*}\in int\left(K\right)$ of $T$ exists. It is proved that a descent-like approximation sequence converges strongly to ${x}^{*}\xb7$ Furthermore, if $K$ is a nonempty closed convex subset of an arbitrary real Banach space and $T:K\to E$ is a uniformly continuous d-weakly contractive map with $F\left(T\right):=\{x\in K:Tx=x\}\ne \varnothing $, it is proved that a descent-like approximation sequence converges strongly to ${x}^{*}\in F\left(T\right)\xb7$