On the convergence of the Ishikawa iterates to a common fixed point of two mappings

Lj. B. Ciric, J. S. Ume and M. S. Khan

Address. Faculty of Mechanical Engineering, Belgrade, Yugoslavia

E-mail: edule@alfa.mas.bg.ac.yu

Abstract. Let $C$ be a convex subset of a complete convex metric space $X$, and $S$ and $T$ be two selfmappings on $C$.
In this paper it is shown that if the sequence of Ishikawa iterations associated with $S$ and $T$ converges, then its limit point is
the common fixed point of $S$ and $T$. This result extends and generalizes the corresponding results of Naimpally and Singh
\cite{6}, Rhoades \cite{7} and Hicks and Kubicek \cite{3}.

AMSclassification. 47H10, 54H25.

Keywords. Ishikawa iterates, comon fixed point, convex metric space.