| MSC: | 47H10 | Fixed-point theorems |
| 47H17 | ||
| 54H25 | Fixed-point and coincidence theorems [See also 47H10, 55M20] |
Abstract:
Let $K$ be a compact convex subset of a real Hilbert space $H$; $%
T:K\rightarrow K$ a continuous hemicontractive map. Let $\{\alpha _{n}\}$ be
a real sequence in $[0,1]$ satisfying appropriate conditions, then for
arbitrary $x_{0}\in K$ and $\{v_{n}\}$ in $K,$ the sequence $\{x_{n}\}$
defined iteratively by $x_{n}=\alpha _{n}x_{n-1}+(1-\alpha _{n})Tv_{n},$ $%
n\geq 1$ converges strongly to a fixed point of $T$.
We also establish a strong convergence of an implicit iteration process to a
common fixed point for a finite family of $\psi -$uniformly
pseudocontractive and $\psi -$uniformly accretive mappings in real Banach
spaces.
The results presented in this paper extend and improve the corresponding
results of Refs. \cite{ari4, ari9, ari19,ari20, ari22, ari25, ari44}.