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Strong convergence theorems of a new hybrid projection method for finite family of two hemi-relatively nonexpansive mappings in a Banach space

Kriengsak Wattanawitoon, Poom Kumam (2011)

Banach Center Publications

In this paper, we prove strong convergence theorems of the hybrid projection algorithms for finite family of two hemi-relatively nonexpansive mappings in a Banach space. Using this result, we also discuss the resolvents of two maximal monotone operators in a Banach space. Our results modify and improve the recently ones announced by Plubtieng and Ungchittrakool [Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space, J. Approx. Theory 149 (2007),...

Strong convergence theorems of k -strict pseudo-contractions in Hilbert spaces

Xiao Long Qin, Shin Min Kang, Mei Juan Shang (2009)

Czechoslovak Mathematical Journal

Let K be a nonempty closed convex subset of a real Hilbert space H such that K ± K ⊂ K , T K → H a k -strict pseudo-contraction for some 0 ≤ k < 1 such that F ( T ) = { x ∈ K x = T x } ≠ ∅ . Consider the following iterative algorithm given by ∀ x 1 ∈ K , x n + 1 = α n γ f ( x n ) + β n x n + ( ( 1 - β n ) I - α n A ) P K S x n , n ≥ 1 , where S K → H is defined by S x = k x + ( 1 - k ) T x , P K is the metric projection of H onto K , A is a strongly positive linear bounded self-adjoint operator, f is a contraction. It is proved that the sequence { x n } generated by the above iterative algorithm converges strongly to a fixed point of T , which solves a variational inequality related...

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