Implicit Mann fixed point iterations for pseudo-contractive mappings

AbstractLet K be a compact convex subset of a real Hilbert space H and T:K→K a continuous hemi-contractive map. Let {an},{bn} and {cn} be real sequences in [0, 1] such that an+bn+cn=1, and {un} and {vn} be sequences in K. In this paper we prove that, if {bn}, {cn} and {vn} satisfy some appropriate conditions, then for arbitrary x0∈K, the sequence {xn} defined iteratively by xn=anxn−1+bnTvn+cnun;n≥1, converges strongly to a fixed point of T