Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical Experiments

Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical Experiments

In this paper, some new modified inertial-type multi-choice CQ-algorithms for approximating common fixed point of countable weakly relatively non-expansive mappings are presented in a real uniformly convex and uniformly smooth Banach space. New proof techniques are used to prove strong convergence t...

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Bibliographic Details
Main Authors: Li Wei, Yibin Xin, Ruilan Zhang, Ravi P. Agarwal
Format: Article
Language:English
Published: MDPI AG 2020-04-01
Series:Mathematics
Subjects:
Lyapunov functional
weakly relatively non-expansive mapping
monotone operator
inertial-type algorithm
multi-choice CQ-algorithm
common fixed point
Online Access:https://www.mdpi.com/2227-7390/8/4/613
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spelling doaj-d9f6199795a64ea992c846e4db57d9e62020-11-25T02:55:57ZengMDPI AGMathematics2227-73902020-04-01861361310.3390/math8040613Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical ExperimentsLi Wei0Yibin Xin1Ruilan Zhang2Ravi P. Agarwal3School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, ChinaSchool of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, ChinaSchool of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, ChinaDepartment of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USAIn this paper, some new modified inertial-type multi-choice CQ-algorithms for approximating common fixed point of countable weakly relatively non-expansive mappings are presented in a real uniformly convex and uniformly smooth Banach space. New proof techniques are used to prove strong convergence theorems, which extend some previous work. The connection and application to maximal monotone operators are demonstrated. Numerical experiments are conducted to illustrate that the rate of convergence is accelerated compared to some previous ones for some special cases.https://www.mdpi.com/2227-7390/8/4/613Lyapunov functionalweakly relatively non-expansive mappingmonotone operatorinertial-type algorithmmulti-choice CQ-algorithmcommon fixed point
collection DOAJ
language English
format Article
sources DOAJ
author Li Wei
Yibin Xin
Ruilan Zhang
Ravi P. Agarwal
spellingShingle Li Wei
Yibin Xin
Ruilan Zhang
Ravi P. Agarwal
Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical Experiments
Mathematics
Lyapunov functional
weakly relatively non-expansive mapping
monotone operator
inertial-type algorithm
multi-choice CQ-algorithm
common fixed point
author_facet Li Wei
Yibin Xin
Ruilan Zhang
Ravi P. Agarwal
author_sort Li Wei
title Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical Experiments
title_short Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical Experiments
title_full Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical Experiments
title_fullStr Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical Experiments
title_full_unstemmed Modified Inertial-Type Multi-Choice CQ-Algorithm for Countable Weakly Relatively Non-Expansive Mappings in a Banach Space, Applications and Numerical Experiments
title_sort modified inertial-type multi-choice cq-algorithm for countable weakly relatively non-expansive mappings in a banach space, applications and numerical experiments
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2020-04-01
description In this paper, some new modified inertial-type multi-choice CQ-algorithms for approximating common fixed point of countable weakly relatively non-expansive mappings are presented in a real uniformly convex and uniformly smooth Banach space. New proof techniques are used to prove strong convergence theorems, which extend some previous work. The connection and application to maximal monotone operators are demonstrated. Numerical experiments are conducted to illustrate that the rate of convergence is accelerated compared to some previous ones for some special cases.
topic Lyapunov functional
weakly relatively non-expansive mapping
monotone operator
inertial-type algorithm
multi-choice CQ-algorithm
common fixed point
url https://www.mdpi.com/2227-7390/8/4/613
work_keys_str_mv AT liwei modifiedinertialtypemultichoicecqalgorithmforcountableweaklyrelativelynonexpansivemappingsinabanachspaceapplicationsandnumericalexperiments
AT yibinxin modifiedinertialtypemultichoicecqalgorithmforcountableweaklyrelativelynonexpansivemappingsinabanachspaceapplicationsandnumericalexperiments
AT ruilanzhang modifiedinertialtypemultichoicecqalgorithmforcountableweaklyrelativelynonexpansivemappingsinabanachspaceapplicationsandnumericalexperiments
AT ravipagarwal modifiedinertialtypemultichoicecqalgorithmforcountableweaklyrelativelynonexpansivemappingsinabanachspaceapplicationsandnumericalexperiments
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