Convergence theorems for ψ-expansive and accretive mappings

Habtu Zegeye, Naseer Shahzad

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Abstract

Let E be a real Banach space, and let A : D (A) ⊆ E → E be a Lipschitz, ψ-expansive and accretive mapping such that over(c o, -) (D (A)) ⊆ ∩λ > 0 R (I + λ A). Suppose that there exists x0 ∈ D (A), where one of the following holds: (i) There exists R > 0 such that ψ (R) > 2 {norm of matrix} A (x0) {norm of matrix}; or (ii) There exists a bounded neighborhood U of x0 such that t (x - x0) ∉ A x for x ∈ ∂ U ∩ D (A) and t < 0. An iterative sequence {xn} is constructed to converge strongly to a zero of A. Related results deal with the strong convergence of this iteration process to fixed points of ψ-expansive and pseudocontractive mappings in real Banach spaces. The convergence results established in this paper are new for this more general class of ψ-expansive and accretive or pseudocontractive mappings.

Original languageEnglish
Pages (from-to)73-82
Number of pages10
JournalNonlinear Analysis, Theory, Methods and Applications
Volume66
Issue number1
DOIs
Publication statusPublished - Jan 1 2007

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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