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

The strong convergence theorems for the split equality fixed point problems in Hilbert spaces

2018 ◽  
Vol 12 (6) ◽  
pp. 255-270
Author(s):  
Jun Niu ◽  
Zheng Zhou ◽  
Jian-Qiang Zhang ◽  
Li-Juan Qin
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Convergence Theorems

scholarly journals Approximating fixed points of demicontractive mappings by iterative methods defined as admissible perturbations

2016 ◽  
Vol 25 (1) ◽  
pp. 121-126
Author(s):  
CRISTINA TICALA ◽  
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Convergence Theorems ◽  
Admissible Perturbation ◽  
Demicontractive Operator ◽  
Demicontractive Mappings ◽  
Fixed Point Iterative Method

The aim of this paper is to prove some convergence theorems for a general Krasnoselskij type fixed point iterative method defined by means of the concept of admissible perturbation of a demicontractive operator in Hilbert spaces.

scholarly journals Approximating fixed points of enriched nonexpansive mappings in Banach spaces by using a retraction-displacement condition

2020 ◽  
Vol 36 (1) ◽  
pp. 27-34 ◽  
Author(s):  
VASILE BERINDE
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Convergence Theorems ◽  
Displacement Condition ◽  
Nonlinear Mappings

In this paper, we prove convergence theorems for a fixed point iterative algorithm of Krasnoselskij-Mann typeassociated to the class of enriched nonexpansive mappings in Banach spaces. The results are direct generaliza-tions of the corresponding ones in [Berinde, V.,Approximating fixed points of enriched nonexpansive mappings byKrasnoselskij iteration in Hilbert spaces, Carpathian J. Math., 35 (2019), No. 3, 293–304.], from the setting of Hilbertspaces to Banach spaces, and also of some results in [Senter, H. F. and Dotson, Jr., W. G.,Approximating fixed pointsof nonexpansive mappings, Proc. Amer. Math. Soc.,44(1974), No. 2, 375–380.], [Browder, F. E., Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl., 20 (1967), 197–228.], byconsidering enriched nonexpansive mappings instead of nonexpansive mappings. Many other related resultsin literature can be obtained as particular instances of our results.

Approximating fixed points of demicontractive mappings by iterative methods defined as admissible perturbations

2016 ◽  
Vol 25 (1) ◽  
pp. 121-126
Author(s):  
CRISTINA TICALA ◽  
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Convergence Theorems ◽  
Admissible Perturbation ◽  
Demicontractive Operator ◽  
Demicontractive Mappings ◽  
Fixed Point Iterative Method

The aim of this paper is to prove some convergence theorems for a general Krasnoselskij type fixed point iterative method defined by means of the concept of admissible perturbation of a demicontractive operator in Hilbert spaces.

scholarly journals Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Jian-Wen Peng ◽  
Yan Wang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems

We introduce an Ishikawa iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007).

scholarly journals Strong Convergence of Modified Inertial Mann Algorithms for Nonexpansive Mappings

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 462
Author(s):  
Bing Tan ◽  
Zheng Zhou ◽  
Songxiao Li
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Convergence Theorems ◽  
Numerical Examples ◽  
Infinite Dimensional

We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.

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