Displaying similar documents to “On the convergence of the Ishikawa iterates to a common fixed point of two mappings”

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

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

Czechoslovak Mathematical Journal

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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...

Asymptotic behavior of solutions of nonlinear difference equations

Janusz Migda (2004)

Mathematica Bohemica

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The nonlinear difference equation x n + 1 - x n = a n ϕ n ( x σ ( n ) ) + b n , ( E ) where ( a n ) , ( b n ) are real sequences, ϕ n ℝ ⟶ ℝ , ( σ ( n ) ) is a sequence of integers and lim n ⟶ ∞ σ ( n ) = ∞ , is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation y n + 1 - y n = b n are given. Sufficient conditions under which for every real constant there exists a solution of equation () convergent to this constant are also obtained.