[HTML][HTML] Implicit Mann fixed point iterations for pseudo-contractive mappings
L Ćirić, A Rafiq, N Cakić, JS Ume - Applied Mathematics Letters, 2009 - Elsevier
L Ćirić, A Rafiq, N Cakić, JS Ume
Applied Mathematics Letters, 2009•ElsevierLet 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.
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.
Let 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.
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