scholarly journals Acceleration of the Halpern algorithm to search for a fixed point of a nonexpansive mapping

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Kaito Sakurai ◽  
Hideaki Iiduka
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Halpern Algorithm

On Asymptotically Nonexpansive Semigroups of Mappings

1970 ◽  
Vol 13 (2) ◽  
pp. 209-214 ◽  
Author(s):  
R. D. Holmes ◽  
P. P. Narayanaswami
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Commutative Semigroups ◽  
Nonexpansive Semigroups ◽  
Asymptotically Nonexpansive ◽  
Cluster Points

A selfmapping f of a metric space (X, d) is nonexpansive (ε-nonexpansive) if d(f(x), f(y)) ≤ d(x, y) for all x, y ∊ X (respectively if d(x, y) < ε). In [1], M. Edelstein proved that a nonexpansive mapping f of En admits a fixed point provided the f-closure of En (i.e. the set of all points which are cluster points of {fn(x)} for some x) is nonempty. R. D. Holmes [2] considered commutative semigroups of selfmappings of a metric space and obtained fixed point theorems for such semigroups under certain contractivity conditions.

scholarly journals Fixed Point Theorems for a New Class of Mappings in Modular Spaces Endowed with a Graph

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Nour-eddine El Harmouchi ◽  
Karim Chaira ◽  
El Miloudi Marhrani
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Fixed Point Theorems ◽  
Iterative Scheme ◽  
Modular Space ◽  
New Class ◽  
Modular Spaces

In this paper, we discuss a class of mappings more general than ρ-nonexpansive mapping defined on a modular space endowed with a graph. In our investigation, we prove the existence of fixed point results of these mappings. Then, we also introduce an iterative scheme for which proves the convergence to a fixed point of such mapping in a modular space with a graph.

scholarly journals Inertial Mann-Type Algorithm for a Nonexpansive Mapping to Solve Monotone Inclusion and Image Restoration Problems

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 750
Author(s):  
Natthaphon Artsawang ◽  
Kasamsuk Ungchittrakool
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Image Restoration ◽  
Zero Point ◽  
Monotone Operators ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Type Method ◽  
Type Algorithm ◽  
Inertial Terms

In this article, we establish a new Mann-type method combining both inertial terms and errors to find a fixed point of a nonexpansive mapping in a Hilbert space. We show strong convergence of the iterate under some appropriate assumptions in order to find a solution to an investigative fixed point problem. For the virtue of the main theorem, it can be applied to an approximately zero point of the sum of three monotone operators. We compare the convergent performance of our proposed method, the Mann-type algorithm without both inertial terms and errors, and the Halpern-type algorithm in convex minimization problem with the constraint of a non-zero asymmetric linear transformation. Finally, we illustrate the functionality of the algorithm through numerical experiments addressing image restoration problems.

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.

WEAK CONVERGENCE OF AN IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR AN ASYMPTOTICALLY QUASI I-NONEXPANSIVE MAPPING IN BANACH SPACES

2011 ◽  
Vol 04 (02) ◽  
pp. 309-319 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Mansoor Saburov
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Nonexpansive Mapping ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Process

In this paper we prove the weak convergence of the implicit iterative process with errors to a common fixed point of an asymptotically quasi I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I in Banach spaces.

scholarly journals On strong convergence theorems for a viscosity-type extragradient method

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 1033-1043
Author(s):  
L.C. Ceng ◽  
C.S. Fong
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Extragradient Method ◽  
Monotone Mapping ◽  
Fixed Point Problem ◽  
Asymptotically Nonexpansive Mapping ◽  
Inclusion Problem ◽  
Point Problem ◽  
Asymptotically Nonexpansive

In this paper, we introduce a general viscosity-type extragradient method for solving the fixed point problem of an asymptotically nonexpansive mapping and the variational inclusion problem with two accretive operators. We obtain a strong convergence theorem in the setting of Banach spaces. In terms of this theorem, we establish the strong convergence result for solving the fixed point problem (FPP) of an asymptotically nonexpansive mapping and the variational inequality problem (VIP) for an inverse-strongly monotone mapping in the framework of Hilbert spaces. Finally, this result is applied to deal with the VIP and FPP in an illustrating example.

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