scholarly journals Robustness of Krasnoselski-Mann's Algorithm for Asymptotically Nonexpansive Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Yu-Chao Tang ◽  
Li-Wei Liu
Keyword(s):  
Banach Space ◽  
Signal Processing ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Asymptotically Nonexpansive Mapping ◽  
Image Recovery ◽  
Iterative Approximation ◽  
Asymptotically Nonexpansive

Iterative approximation of fixed points of nonexpansive mapping is a very active theme in many aspects of mathematical and engineering areas, in particular, in image recovery and signal processing. Because the errors usually occur in few places, it is necessary to show that whether the iterative algorithm is robust or not. In the present work, we prove that Krasnoselski-Mann's algorithm is robust for asymptotically nonexpansive mapping in a Banach space setting. Our results generalize the corresponding results existing in the literature.

The Strong Convergence of a New Iterative Algorithm for Asymptotically Nonexpansive Mappings

2013 ◽  
Vol 756-759 ◽  
pp. 3628-3633
Author(s):  
Yuan Heng Wang ◽  
Wei Wei Sun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Real Banach Space ◽  
Nonexpansive Mappings ◽  
Iterative Sequence ◽  
Asymptotically Nonexpansive ◽  
Differentiable Norm

In a real Banach space E with a uniformly differentiable norm, we prove that a new iterative sequence converges strongly to a fixed point of an asymptotically nonexpansive mapping. The results in this paper improve and extend some recent results of other authors.

scholarly journals A New Hybrid Algorithm for Solving a System of Generalized Mixed Equilibrium Problems, Solving a Family of Quasi--Asymptotically Nonexpansive Mappings, and Obtaining Common Fixed Points in Banach Space

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
J. F. Tan ◽  
S. S. Chang
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Generalized Mixed Equilibrium Problems ◽  
Asymptotically Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

The main purpose of this paper is to introduce a new hybrid iterative scheme for finding a common element of set of solutions for a system of generalized mixed equilibrium problems, set of common fixed points of a family of quasi--asymptotically nonexpansive mappings, and null spaces of finite family of -inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. The results presented in the paper improve and extend the corresponding results announced by some authors.

scholarly journals Characterizations of fixed points of nonexpansive mappings

2005 ◽  
Vol 2005 (11) ◽  
pp. 1723-1735 ◽  
Author(s):  
Tomonari Suzuki
Keyword(s):  
Banach Space ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Strict Convexity ◽  
Banach Limit ◽  
Banach Limits

Using the notion of Banach limits, we discuss the characterization of fixed points of nonexpansive mappings in Banach spaces. Indeed, we prove that the two sets of fixed points of a nonexpansive mapping and some mapping generated by a Banach limit coincide. In our discussion, we may not assume the strict convexity of the Banach space.

scholarly journals Inertial Accelerated Algorithm for Fixed Point of Asymptotically Nonexpansive Mapping in Real Uniformly Convex Banach Spaces

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 147
Author(s):  
Murtala Haruna Harbau ◽  
Godwin Chidi Ugwunnadi ◽  
Lateef Olakunle Jolaoso ◽  
Ahmad Abdulwahab
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Convex Banach Space ◽  
Asymptotically Nonexpansive Mapping ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Uniformly Convex Banach Spaces ◽  
Asymptotically Nonexpansive ◽  
Mann Algorithm

In this work, we introduce a new inertial accelerated Mann algorithm for finding a point in the set of fixed points of asymptotically nonexpansive mapping in a real uniformly convex Banach space. We also establish weak and strong convergence theorems of the scheme. Finally, we give a numerical experiment to validate the performance of our algorithm and compare with some existing methods. Our results generalize and improve some recent results in the literature.

An ergodic theorem for asymptotically nonexpansive mappings

1994 ◽  
Vol 124 (1) ◽  
pp. 23-31
Author(s):  
Manfred Krüppel ◽  
Jaroslaw Górnicki
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Ergodic Theorem ◽  
Convex Subset ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive ◽  
Image Position

The purpose of this paper is to prove the following (nonlinear) mean ergodic theorem: Let E be a uniformly convex Banach space, let C be a nonempty bounded closed convex subset of E and let T: C → C be an asymptotically nonexpansive mapping. Ifexists uniformly in r = 0, 1, 2,…, then the sequence {Tnx} is strongly almost-convergent to a fixed point y of T, that is,uniformly in i = 0, 1, 2, ….

Two-step iterative approximation of common fixed points of two nonself asymptotically quasi-nonexpansive mappings

2015 ◽  
Vol 08 (03) ◽  
pp. 1550060
Author(s):  
Amit Singh ◽  
R. C. Dimri ◽  
Darshana J. Prajapati
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Iterative Approximation ◽  
Convergence Theorems ◽  
Strong And Weak Convergence

In this paper, we study an iterative approximation of common fixed points of two nonself asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in a uniformly convex Banach space.

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