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Common Fixed Points Iteration Processes for a Finite Family of Asymptotically Nonexpansive Mappings
-
Jui-Chi Huang
Veröffentlicht/Copyright:
3. März 2010
Abstract
Let 𝐸 be a uniformly convex Banach space which satisfies Opial's condition or its dual 𝐸* has the Kadec–Klee property, 𝐶 a nonempty closed convex subset of 𝐸, and 𝑇𝑗 : 𝐶 → 𝐶 an asymptotically nonexpansive mapping for each 𝑗 = 1, 2, . . . , 𝑟. Suppose {𝑥𝑛} is generated iteratively by
where 
𝑈𝑛(0) = 𝐼, 𝐼 is the identity map and {α𝑛(𝑗)} is a suitable sequence in [0, 1]. If the set 
of common fixed points of 
is nonempty, then weak convergence of {𝑥𝑛} to some 
is obtained.
Key words and phrases:: Asymptotically nonexpansive mapping; Fixed point; uniformly convex Banach space; Opial's condition; Kadec–Klee property
Received: 2003-09-04
Revised: 2003-12-04
Published Online: 2010-03-03
Published in Print: 2004-March
© Heldermann Verlag
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Schlagwörter für diesen Artikel
Asymptotically nonexpansive mapping;
Fixed point;
uniformly convex Banach space;
Opial's condition;
Kadec–Klee property
Artikel in diesem Heft
- Some Integral Operators which Preserve a Subclass of Uniformly Quasiconvex Functions
- Linearization and Higher Order Nonlinear Oscillation Theorems Using Comparison Methods
- The Structure of 𝐺-Free Nilpotent Groups of Step 3
- Fuzzy Solutions for Neutral Functional Differential Equations with Nonlocal Conditions
- Projective Bundles on Infinite-Dimensional Complex Spaces
- Explicit Solutions of the Basic Boundary Value Problems of Statics of the Elastic Mixture Theory for an Annulus
- Particular Solutions for a Class of ODE Related to the L-Exponential Functions
- On Hyers–Ulam Stability of Cauchy and Wilson Equations
- Common Fixed Points Iteration Processes for a Finite Family of Asymptotically Nonexpansive Mappings
- Varieties of Universal Algebras with Normal Local Projections
- Integrability and L1-Convergence of Modified Sine Sums
- On Homogeneous Coverings of Euclidean Spaces
- On Entire Modular Forms of Half-Integral Weight on the Congruence Subgroup Γ0(4N)
- The Bellman Equation Related to the Minimal Entropy Martingale Measure
- Oscillation and Nonoscillation Criteria for two-Dimensional Systems of Linear Ordinary Differential Equations
- Formulas of Variation for a Solution of Neutral Differential Equations with Continuous Initial Condition
- Positive Solutions of a Neutral Difference Equation with Positive and Negative Coefficients
- Two Sharp Inequalities of Simpson Type and Applications
- On the Equivalence between Ch and The Existence of Certain I-Luzin Subsets of ℝ
