Strong convergence theorems for strict pseudo-contractions in image-uniformly smooth Banach spaces Original Research Article

Let CC be a closed convex subset of a real qq-uniformly smooth Banach space and Ti:C→CTi:C→C, i=1,2,…,Ni=1,2,…,N be a finite family of mappings which are strictly pseudo-contractive. Assume View the MathML sourceF≔⋂i=1NF(Ti)≠0̸. Let u,x0∈Cu,x0∈C be arbitrary fixed vectors in CC. It is proved that the sequence {xn}n≥0{xn}n≥0 generated by View the MathML source{yn=(1−αn)xn+αn∑i=1Nηi(n)Tixn,xn+1=βnu+γnxn+δnyn, Turn MathJax on where {αn}{αn}, {βn}{βn}, {γn}{γn} and {σn}{σn} are sequences in (0,1)(0,1) satisfying appropriate conditions, converges strongly to an element of FF.