Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems
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 algo...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2020-02-01
|
Series: | Mathematics |
Subjects: | |
Online Access: | https://www.mdpi.com/2227-7390/8/2/236 |
id |
doaj-18c068eb581341e4a0d9fe80fda4f61c |
---|---|
record_format |
Article |
spelling |
doaj-18c068eb581341e4a0d9fe80fda4f61c2020-11-25T02:33:37ZengMDPI AGMathematics2227-73902020-02-018223610.3390/math8020236math8020236Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point ProblemsBing Tan0Shanshan Xu1Songxiao Li2Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, ChinaInstitute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, ChinaIn 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.https://www.mdpi.com/2227-7390/8/2/236conjugate gradient methodsteepest descent methodhybrid projectionshrinking projectioninertial mannstrongly convergencenonexpansive mapping |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Bing Tan Shanshan Xu Songxiao Li |
spellingShingle |
Bing Tan Shanshan Xu Songxiao Li Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems Mathematics conjugate gradient method steepest descent method hybrid projection shrinking projection inertial mann strongly convergence nonexpansive mapping |
author_facet |
Bing Tan Shanshan Xu Songxiao Li |
author_sort |
Bing Tan |
title |
Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems |
title_short |
Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems |
title_full |
Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems |
title_fullStr |
Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems |
title_full_unstemmed |
Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems |
title_sort |
modified inertial hybrid and shrinking projection algorithms for solving fixed point problems |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2020-02-01 |
description |
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. |
topic |
conjugate gradient method steepest descent method hybrid projection shrinking projection inertial mann strongly convergence nonexpansive mapping |
url |
https://www.mdpi.com/2227-7390/8/2/236 |
work_keys_str_mv |
AT bingtan modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems AT shanshanxu modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems AT songxiaoli modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems |
_version_ |
1724812730126303232 |