Viscosity approximation methods for a common fixed point of finite family of nonexpansive mappings

Habtu Zegeye, Naseer Shahzad

Research output: Contribution to journalArticle

24 Citations (Scopus)


Let K be a nonempty closed and convex subset of a real Banach space E. Let T : K → E be a nonexpansive weakly inward mapping with F (T) ≠ ∅ and f : K → K be a contraction. Then for t ∈ (0, 1), there exists a sequence {yt} ⊂ K satisfying yt = (1 - t) f (yt) + tT (yt). Furthermore, if E is a strictly convex real reflexive Banach space having a uniformly Gâteaux differentiable norm, then {yt} converges strongly to a fixed point p of T such that p is the unique solution in F (T) to a certain variational inequality. Moreover, if {Ti, i = 1, 2, ..., r} is a family of nonexpansive mappings, then an explicit iteration process which converges strongly to a common fixed point of {Ti, i = 1, 2, ..., r} and to a solution of a certain variational inequality is constructed. Under the above setting, the family Ti, i = 1, 2, ..., r need not satisfy the requirment that {Mathematical expression}.

Original languageEnglish
Pages (from-to)155-163
Number of pages9
JournalApplied Mathematics and Computation
Issue number1
Publication statusPublished - Aug 1 2007


All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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