scholarly journals Convergence of an inertial-type Krasnosel’skii-Mann-type iterative sequence to fixed points of nonexpansive mappings in Hilbert spaces

2021 ◽  
Keyword(s):  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Sequence

scholarly journals On the viscosity rule for common fixed points of two nonexpansive mappings in Hilbert spaces

2017 ◽  
Vol 1 (1) ◽  
pp. 111-125 ◽  
Author(s):  
Sayed Fakhar Abbas Naqvi ◽  
◽  
Muhammad Saqib Khan ◽  
Keyword(s):  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points

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.

scholarly journals A Modified Krasnosel’skiǐ–Mann Iterative Algorithm for Approximating Fixed Points of Enriched Nonexpansive Mappings

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 123
Author(s):  
Vasile Berinde
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Fixed Point Algorithm ◽  
Mann Algorithm

For approximating the fixed points of enriched nonexpansive mappings in Hilbert spaces, we consider a modified Krasnosel’skiǐ–Mann algorithm for which we prove a strong convergence theorem. We also empirically compare the rate of convergence of the modified Krasnosel’skiǐ–Mann algorithm and of the simple Krasnosel’skiǐ fixed point algorithm. Based on the numerical experiments reported in the paper we conclude that, for the class of enriched nonexpansive mappings, it is more convenient to work with the simple Krasnosel’skiǐ fixed point algorithm than with the modified Krasnosel’skiǐ–Mann algorithm.

scholarly journals A General Inertial Viscosity Type Method for Nonexpansive Mappings and Its Applications in Signal Processing

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 288 ◽  
Author(s):  
Yinglin Luo ◽  
Meijuan Shang ◽  
Bing Tan
Keyword(s):  
Signal Processing ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Type Method ◽  
Pseudocontractive Mappings ◽  
Inertia Parameters ◽  
Strictly Pseudocontractive Mappings

In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.

scholarly journals Computing the Fixed Points of Strictly Pseudocontractive Mappings by the Implicit and Explicit Iterations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yeong-Cheng Liou
Keyword(s):  
Fixed Point ◽  
Inverse Problems ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Minimum Norm ◽  
Pseudocontractive Mappings ◽  
Special Cases ◽  
Implicit And Explicit ◽  
Strictly Pseudocontractive Mappings

It is known that strictly pseudocontractive mappings have more powerful applications than nonexpansive mappings in solving inverse problems. In this paper, we devote to study computing the fixed points of strictly pseudocontractive mappings by the iterations. Two iterative methods (one implicit and another explicit) for finding the fixed point of strictly pseudocontractive mappings have been constructed in Hilbert spaces. As special cases, we can use these two methods to find the minimum norm fixed point of strictly pseudocontractive mappings.

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