Strong convergence for the modified Mann’s iteration of [formula omitted]-strict pseudocontraction

Abstract

In this paper, for an λ-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],where {αn},{βn} and {γn} in (0,1) satisfy:(i)0⩽αn⩽λK2 with liminfn→∞αn(λ-K2αn)>0;(ii)limn→∞βn=0 and ∑n=1∞βn=∞;(iii)limsupn→∞γn<1.Our results unify and improve some existing results.