Iterative construction of a common fixed point of finite families of nonlinear mappings
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Abstract
Let K be a nonempty closed convex subset of a real reflexive Banach space E with uniformly Gâteuax differentiable norm. Let T1, T2, . . . , Tm : K → K be m Lipschitz mappings (for some m ∈ ℕ) such that 
. We construct a new iteration process and prove that the iteration process converges strongly to a common fixed point of these mappings provided at least one of the mappings is pseudocontractive. We also obtain as easy corollaries convergence results for finite families of Lipschitz pseudocontractive mappings and nonexpansive mappings. Furthermore, We prove that a slight modification of our iteration process converges strongly to a common zero of a finite family of Lipschitz accretive operators. Our new iteration process and our method of proof are of independent interest.
© de Gruyter 2010
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Articles in the same Issue
- Approximation for fixed points of strict pseudo-contractions and solutions of equilibrium and optimization problems
- Some applications of dominated convergence theorems to a higher-order singular boundary value problem
- Fractional white noise perturbations of parabolic Volterra equations
- Optimality and duality for nonsmooth multiobjective optimization problems with generalized V -r-invexity
- Iterative construction of a common fixed point of finite families of nonlinear mappings
- Some algebraic properties of theWiener–Laplace algebra
- Fair valuation of universal life policies via a replicating portfolio
- Positive solutions for discrete boundary value problems with p-Laplacian
- A composite functional equation and invariant curves
- Collections of Darboux-like, Baire one functions of two variables
- Čech-completeness and related properties of the generalized compact-open topology
