Approximation of minimum-norm fixed point of total asymptotically nonexpansive mapping

2014 ◽  
Vol 26 (5-6) ◽  
pp. 699-715 ◽  
Author(s):  
E. U. Ofoedu ◽  
A. C. Nnubia
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Asymptotically Nonexpansive Mapping ◽  
Minimum Norm ◽  
Total Asymptotically Nonexpansive Mapping ◽  
Asymptotically Nonexpansive

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.

scholarly journals Approximation of common solutions for a fixed point problem of asymptotically nonexpansive mapping and a generalized equilibrium problem in Hilbert space

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Richard Osward ◽  
Santosh Kumar ◽  
Mengistu Goa Sangago
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Equilibrium Problem ◽  
Fixed Point Problem ◽  
Asymptotically Nonexpansive Mapping ◽  
Point Problem ◽  
Generalized Equilibrium Problem ◽  
Common Solution ◽  
Asymptotically Nonexpansive ◽  
Generalized Equilibrium

Abstract In this paper, we introduce an iterative algorithm to approximate a common solution of a generalized equilibrium problem and a fixed point problem for an asymptotically nonexpansive mapping in a real Hilbert space. We prove that the sequences generated by the iterative algorithm converge strongly to a common solution of the generalized equilibrium problem and the fixed point problem for an asymptotically nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in this research area. Some applications of main results are also provided.

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.

scholarly journals A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Preedaporn Kanjanasamranwong ◽  
Poom Kumam ◽  
Siwaporn Saewan
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Asymptotically Nonexpansive Mapping ◽  
Point Problem ◽  
Common Solution ◽  
Asymptotically Nonexpansive ◽  
System Of Equilibrium Problems

The purpose of this paper is to introduce the modified Halpern-type iterative method by the generalizedf-projection operator for finding a common solution of fixed-point problem of a totally quasi-ϕ-asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Consequently, we prove the strong convergence for a common solution of above two sets. Our result presented in this paper generalize and improve the result of Chang et al., (2012), and some others.

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.

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.

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