SPLIT COMMON FIXED POINT PROBLEM FOR CLASS OF ASYMPTOTICALLY HEMICONTRACTIVE MAPPINGS

E. E. CHIMA, M. O. OSILIKE

Abstract


Let $H_1$ and $H_2$ be two real Hilbert spaces. $T:H_1\rightarrow H_1$ and $S:H_2\rightarrow H_2$ two asymptotically hemicontractive maps. Let $A:H_1\rightarrow H_2$ be a bounded linear operator. The split common fixed point problem (SCFP) for $T$ and $S$, which is to find a fixed point $x^*\in F(T)$ such that $Ax^*\in F(S)$ is studied. We proved that the set of fixed points of a class of  asymptotically hemicontractive maps is closed and convex. We then obtain strong convergence results for the SCFP involving two asymtotically hemicontractive maps using new averaging iterative scheme.

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