Implicit Mann fixed point iterations for pseudo-contractive mappings

Let KK be a compact convex subset of a real Hilbert space HH and T:K→KT:K→K a continuous hemi-contractive map. Let {an},{bn}{an},{bn} and {cn}{cn} be real sequences in [0, 1] such that an+bn+cn=1an+bn+cn=1, and {un}{un} and {vn}{vn} be sequences in KK. In this paper we prove that, if {bn}{bn}, {cn}{cn} and {vn}{vn} satisfy some appropriate conditions, then for arbitrary x0∈Kx0∈K, the sequence {xn}{xn} defined iteratively by xn=anxn−1+bnTvn+cnun;n≥1xn=anxn−1+bnTvn+cnun;n≥1, converges strongly to a fixed point of TT.