Acta Mathematica Sinica, English Series

, Volume 24, Issue 3, pp 463–470 | Cite as

Convergence analysis of iterative sequences for a pair of mappings in Banach spaces

Article

Abstract

Let C be a nonempty closed convex subset of a real Banach space E. Let S: CC be a quasi-nonexpansive mapping, let T: CC be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F:= {x ε C: Sx = x and Tx = x} ≠ 0. Let {xn}n≥0 be the sequence generated from an arbitrary x0 ε C by
$$ x_{n + 1} = (1 - c_n )Sx_n + c_n T^n x_n , n \geqslant 0. $$
We prove the necessary and sufficient conditions for the strong convergence of the iterative sequence {xn} to an element of F. These extend and improve the recent results of Moore and Nnoli.

Keywords

quasi-nonexpansive mapping asymptotically demicontractive type mapping iterative sequence convergence analysis 

MR(2000) Subject Classification

47H09 47H10 47H17 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiP. R. China
  2. 2.Department of Applied MathematicsNational Sun Yat-Sen UniversityKaohsiungChina

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