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Approximating Common Fixed Points of Nonexpansive Mappings in Banach Spaces
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Naseer Shahzad
Veröffentlicht/Copyright:
10. März 2010
Abstract
Let 𝐾 be a nonempty closed convex subset of a real uniformly convex Banach space 𝐸 and 𝑆, 𝑇 : 𝐾 → 𝐾 two nonexpansive mappings such that 𝐹(𝑆) ∩ 𝐹(𝑇) := {𝑥 ∈ 𝐾 : 𝑆𝑥 = 𝑇𝑥 = 𝑥} ≠ ø. Suppose {𝑥𝑛} is generated iteratively by
𝑥1 ∈ 𝐾, 𝑥𝑛+1 = (1 – α𝑛)𝑥𝑛 + α𝑛𝑆[(1 – β𝑛)𝑥𝑛 + β𝑛𝑇𝑥𝑛],
𝑛 ≥ 1, where {α𝑛}, {β𝑛} are real sequences in [0, 1]. In this paper, we discuss the weak and strong convergence of {𝑥𝑛} to some 𝑥* ∈ 𝐹(𝑆) ∩ 𝐹(𝑇).
Received: 2005-12-24
Revised: 2006-02-12
Published Online: 2010-03-10
Published in Print: 2006-September
© Heldermann Verlag
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Artikel in diesem Heft
- Global Existence and Energy Decay of Solutions to a Petrovsky Equation with General Nonlinear Dissipation and Source Term
- Curves with Two Pencils and Associated Maps to Projective Spaces
- The Second Obstruction Functor
- Ground State Solutions of Nonlinear Stationary Schrödinger Systems with Discontinuous Nonlinearity and Variable Potential
- Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–Fourier Series
- On the Convergence of Conjugate Trigonometric Polynomials
- Existence of Solutions for Fourth Order Nonlocal Boundary Value Problems
- New Proof of the 𝑇(1) Theorem for Triebel–Lizorkin Spaces
- Inversion of Ahlfors and Grunsky Inequalities
- On Non-Compact Operators in Weighted Ideal and Symmetric Function Spaces
- Computing Characteristic Sets of Ordinary Radical Differential Ideals
- Approximating Common Fixed Points of Nonexpansive Mappings in Banach Spaces
- On Systems of Linear Functional Differential Inequalities
- The Dirichlet Problem for a Second Order Elliptic Equation Degenerating on the Whole Boundary When the Boundary Condition Is Satisfied in the Presence of Some Weight
- Fourier Series with Small Gaps
- Oscillations of Higher Order Functional Differential Equations with Impulses
