Strong convergence for the modified Mann’s iteration of λλ-strict pseudocontraction

In this paper, for an λλ-strict pseudocontraction T, we prove strong convergence of the modified Mann’s iteration defined byxn+1=βnu+γnxn+(1-βn-γn)[αnTxn+(1-αn)xn],xn+1=βnu+γnxn+(1-βn-γn)[αnTxn+(1-αn)xn],where {αn},{βn} and {γn}{γn} in (0,1)(0,1) satisfy:(i)0⩽αn⩽λK2 with liminfn→∞αn(λ-K2αn)>0liminfn→∞αn(λ-K2αn)>0;(ii)limn→∞βn=0limn→∞βn=0 and ∑n=1∞βn=∞;(iii)limsupn→∞γn<1limsupn→∞γn<1.Our results unify and improve some existing results.