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...

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Main Authors: Bing Tan, Shanshan Xu, Songxiao Li
Format: Article
Language:English
Published: MDPI AG 2020-02-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/8/2/236
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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
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