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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...

Structure of stable solutions of a one-dimensional variational problem

Nung Kwan Yip (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double...

Study of a viscoelastic frictional contact problem with adhesion

Arezki Touzaline (2011)

Commentationes Mathematicae Universitatis Carolinae

We consider a quasistatic frictional contact problem between a viscoelastic body with long memory and a deformable foundation. The contact is modelled with normal compliance in such a way that the penetration is limited and restricted to unilateral constraint. The adhesion between contact surfaces is taken into account and the evolution of the bonding field is described by a first order differential equation. We derive a variational formulation and prove the existence and uniqueness result of the...

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