Iterative approximation of fixed points for a family of quasi-nonexpansive mappings
Song Na-na · Journal of Shenyang Normal University · 2012
In recent years,the scholars on the fixed point study of quasi-nonexpansive mapping are more and more active,and iterative scheme is also more and more rich,but the algorithm on family of nonexpansive of fixed point iterative scheme are more complicated.In this paper,the purpose is to find a better solution to combine family of quasi-nonexpansive mapping of fixed point.In real Hilbert space an modification of iterative program is introduced to combine the common element of two sets,which are family of quasi-nonexpansive mapping.Under appropriate conditions,and by using new hybrid iteration scheme we prove strong convergence theorem on family of quasi-nonexpansive mapping of fixed point.This is a new iterative algorithm to construct family of quasi-nonexpansive mapping of fixed point without making use of demi-closedness property for mapping T,but it is easier and more general than later.It is also the direction of study on iterative scheme.Therefore,this paper can be a reference for iteration scheme later.