The paper concerns some generalizations of convergence of special type of iterations of asymptotically nonexpansive mappings in uniformly convex Banach spaces to a fixed point.
A map defined on a subset of a Banach space is said to be asymptotically nonexpansive iff
for all and , where is a sequence of real numbers such that
The author considers the convergence of the following iteration process with errors
where and are sequences in satisfying
and and are sequences of real numbers in .
Under some additional assumptions it has been proved that the sequence of iterations converges strongly to a fixed point of .
The results presented here are some generalizations of the results obtained in 1994 by B. E. Rhoades.
Let’s note that some facts (see e.g. Lemma 1, Lemma 6) proved in the paper are very obvious.