System of implicit iteration for fixed points of a finite family of strictly pseudocontractive mappings
Suhong Li · 2005
Let E be real Banach space and K a nonempty convex subset of E, and let {Ti}i=1N be a finite family of Strictly pseudocontractive self-maps of K, for x0∈K, a new system of implicit iteration process is put forward as following xn=αnxn-1+(1-αn)Tnyn yn=βnxn-1+(1-βn)Tnxn Where Tn=TnmodN,n≥1,{αn},{βn}(?)[0,1]. The problems of approximating fixed points of strictly pseudcon-traclive mappings in an arbitrary real Banach spaces by this new interation sequence is investigated. Meanwhile , strong convergent theorems are also proved.