Fixed Points Approximation for Non Expansive Operators in Hilbert Spaces

Abstract

Approximations of fixed points have been done in different space and classes. However, characterizations in norm attainable classes remain interesting. This paper discusses approximation of nonexpansive operators in Hilbert spaces in terms of fixed points. In particular, we prove that for an invariant subspace H0 of a complex Hilbert space H; there exists a unique nonexpansive retraction R of H0 onto _(Q) and x 2 H0 such that the sequence f_ng generated by _n =_nf(_n)+(1_n)T_n_n is strongly convergent to Rx for all n 2 N .