mann algorithm
Recently Published Documents


TOTAL DOCUMENTS

18
(FIVE YEARS 4)

H-INDEX

4
(FIVE YEARS 0)

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 123
Author(s):  
Vasile Berinde

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.


Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 147
Author(s):  
Murtala Haruna Harbau ◽  
Godwin Chidi Ugwunnadi ◽  
Lateef Olakunle Jolaoso ◽  
Ahmad Abdulwahab

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.


Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 51
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas ◽  
Manuel de la Sen

We propose two new iterative algorithms for solving K-pseudomonotone variational inequality problems in the framework of real Hilbert spaces. These newly proposed methods are obtained by combining the viscosity approximation algorithm, the Picard Mann algorithm and the inertial subgradient extragradient method. We establish some strong convergence theorems for our newly developed methods under certain restriction. Our results extend and improve several recently announced results. Furthermore, we give several numerical experiments to show that our proposed algorithms performs better in comparison with several existing methods.


Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 638
Author(s):  
Yekini Shehu ◽  
Aviv Gibali

In this paper, we give a general inertial Krasnoselskii–Mann algorithm for solving inclusion problems in Banach Spaces. First, we establish a weak convergence in real uniformly convex and q-uniformly smooth Banach spaces for finding fixed points of nonexpansive mappings. Then, a strong convergence is obtained for the inertial generalized forward-backward splitting method for the inclusion. Our results extend many recent and related results obtained in real Hilbert spaces.


Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 236 ◽  
Author(s):  
Bing Tan ◽  
Shanshan Xu ◽  
Songxiao Li

In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.


2019 ◽  
Vol 38 (9) ◽  
pp. 2114-2126 ◽  
Author(s):  
Yizun Lin ◽  
C. Ross Schmidtlein ◽  
Qia Li ◽  
Si Li ◽  
Yuesheng Xu

Sign in / Sign up

Export Citation Format

Share Document