scholarly journals Approximation of viscosity zero points of accretive operators in a Banach space

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2175-2184
Author(s):  
Sun Cho ◽  
Shin Kang
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Accretive Operators ◽  
Convergence Theorems ◽  
Computational Errors ◽  
Zero Points

In this paper, zero points of m-accretive operators are investigated based on a viscosity iterative algorithm with double computational errors. Strong convergence theorems for zero points of m-accretive operators are established in a Banach space.

A forward-backward iterative method for zero points of sum of two accretive operators

2017 ◽  
Vol 33 (3) ◽  
pp. 353-363
Author(s):  
XIAOLONG QIN ◽  
◽  
QAMRUL HASAN ANSARI ◽  
JEN-CHIH YAO ◽  
◽  
...  
Keyword(s):  
Strong Convergence ◽  
Zero Point ◽  
Point Problem ◽  
Accretive Operators ◽  
Uniformly Smooth ◽  
Convergence Results ◽  
Convex Minimization Problems ◽  
Computational Errors ◽  
Uniformly Smooth Banach Spaces ◽  
Zero Points

In this paper, we study a zero point problem of the sum of two accretive operators based on a viscosity forwardbackward iterative algorithm with computational errors. Strong convergence results are established in the framework of q-uniformly smooth Banach spaces. We also apply the strong convergence results to solve variational inequality problems, convex minimization problems and fixed point problems.

scholarly journals Approximation of Solutions of an Equilibrium Problem in a Banach Space

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Hecai Yuan ◽  
Guohong Shi
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Smooth Banach Space ◽  
Convergence Theorems ◽  
Strictly Convex ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth

An equilibrium problem is investigated based on a hybrid projection iterative algorithm. Strong convergence theorems for solutions of the equilibrium problem are established in a strictly convex and uniformly smooth Banach space which also enjoys the Kadec-Klee property.

scholarly journals Strong Convergence Theorems for Asymptotically WeakG-Pseudo-Ψ-Contractive Non-Self-Mappings with the Generalized Projection in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yuanheng Wang
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Approximation Method ◽  
Generalized Projection ◽  
Iterative Sequence ◽  
Successive Approximation Method ◽  
Convergence Theorems ◽  
Mann Iterative Sequence ◽  
Sequence Method ◽  
Generalized Projection Method

A new concept of the asymptotically weakG-pseudo-Ψ-contractive non-self-mappingT:G↦Bis introduced and some strong convergence theorems for the mapping are proved by using the generalized projection method combined with the modified successive approximation method or with the modified Mann iterative sequence method in a uniformly and smooth Banach space. The proof methods are also different from some past common methods.

scholarly journals Strong convergence of an inertial forward-backward splitting method for accretive operators in real Banach space

2020 ◽  
Vol 21 (2) ◽  
pp. 397-412 ◽  
Author(s):  
H.A. Abass ◽  
◽  
C. Izuchukwu ◽  
O.T. Mewomo ◽  
Q.L. Dong ◽  
...  
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Real Banach Space ◽  
Splitting Method ◽  
Accretive Operators

scholarly journals Convergence of Two Splitting Projection Algorithms in Hilbert Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 922
Author(s):  
Marwan A. Kutbi ◽  
Abdul Latif ◽  
Xiaolong Qin
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Monotone Mappings ◽  
Projection Algorithms ◽  
Convergence Theorems ◽  
Expansive Mapping ◽  
Computational Errors ◽  
Zero Points

The aim of this present paper is to study zero points of the sum of two maximally monotone mappings and fixed points of a non-expansive mapping. Two splitting projection algorithms are introduced and investigated for treating the zero and fixed point problems. Possible computational errors are taken into account. Two convergence theorems are obtained and applications are also considered in Hilbert spaces

scholarly journals Iterative methods for zero points of accretive operators in Banach spaces

2012 ◽  
Vol 20 (1) ◽  
pp. 329-344
Author(s):  
Sheng Hua Wang ◽  
Sun Young Cho ◽  
Xiao Long Qin
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Convex Function ◽  
Real Banach Space ◽  
Real Hilbert Space ◽  
Lower Semicontinuous ◽  
Iterative Algorithms ◽  
Accretive Operators ◽  
Weak And Strong Convergence ◽  
Zero Points

Abstract The purpose of this paper is to consider the problem of approximating zero points of accretive operators. We introduce and analysis Mann-type iterative algorithm with errors and Halpern-type iterative algorithms with errors. Weak and strong convergence theorems are established in a real Banach space. As applications, we consider the problem of approximating a minimizer of a proper lower semicontinuous convex function in a real Hilbert space

scholarly journals Strong convergence theorems for a sequence of nonexpansive mappings with gauge functions

2013 ◽  
Vol 21 (1) ◽  
pp. 183-200
Author(s):  
Prasit Cholamjiak ◽  
Yeol Je Cho ◽  
Suthep Suantai
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Convex Banach Space ◽  
Duality Mapping ◽  
Convergence Theorems ◽  
Strictly Convex Banach Space ◽  
Differentiable Norm ◽  
Gauge Functions

Abstract In this paper, we first prove a path convergence theorem for a nonexpansive mapping in a reflexive and strictly convex Banach space which has a uniformly Gˆateaux differentiable norm and admits the duality mapping jφ, where φ is a gauge function on [0,∞). Using this result, strong convergence theorems for common fixed points of a countable family of nonexpansive mappings are established.

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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