Several Fixed Point Theorems in Convex <i>b</i>-Metric Spaces and Applications

Several Fixed Point Theorems in Convex <i>b</i>-Metric Spaces and Applications

Our paper is devoted to indicating a way of generalizing Mann&#8217;s iteration algorithm and a series of fixed point results in the framework of <i>b</i>-metric spaces. First, the concept of a convex <i>b</i>-metric space by means of a convex structure is introduced and...

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Main Authors: Lili Chen, Chaobo Li, Radoslaw Kaczmarek, Yanfeng Zhao
Format: Article
Language:English
Published: MDPI AG 2020-02-01
Series:Mathematics
Subjects:
b-metric space
mann’s iteration scheme
fixed point theorems
convex structure
Online Access:https://www.mdpi.com/2227-7390/8/2/242
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spelling doaj-cc6d7d6831cd46fbbb935a1cce57e8e12020-11-25T01:30:42ZengMDPI AGMathematics2227-73902020-02-018224210.3390/math8020242math8020242Several Fixed Point Theorems in Convex <i>b</i>-Metric Spaces and ApplicationsLili Chen0Chaobo Li1Radoslaw Kaczmarek2Yanfeng Zhao3College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaDepartment of Mathematics, Harbin University of Science and Technology, Harbin 150080, ChinaPoznań, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Uniwersytetu Poznańskiego 4, 61-614 Poznań, PolandCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaOur paper is devoted to indicating a way of generalizing Mann&#8217;s iteration algorithm and a series of fixed point results in the framework of <i>b</i>-metric spaces. First, the concept of a convex <i>b</i>-metric space by means of a convex structure is introduced and Mann&#8217;s iteration algorithm is extended to this space. Next, by the help of Mann&#8217;s iteration scheme, strong convergence theorems for two types of contraction mappings in convex <i>b</i>-metric spaces are obtained. Some examples supporting our main results are also presented. Moreover, the problem of the <i>T</i>-stability of Mann&#8217;s iteration procedure for the above mappings in complete convex <i>b</i>-metric spaces is considered. As an application, we apply our main result to approximating the solution of the Fredholm linear integral equation.https://www.mdpi.com/2227-7390/8/2/242b-metric spacemann’s iteration schemefixed point theoremsconvex structure
collection DOAJ
language English
format Article
sources DOAJ
author Lili Chen
Chaobo Li
Radoslaw Kaczmarek
Yanfeng Zhao
spellingShingle Lili Chen
Chaobo Li
Radoslaw Kaczmarek
Yanfeng Zhao
Several Fixed Point Theorems in Convex <i>b</i>-Metric Spaces and Applications
Mathematics
b-metric space
mann’s iteration scheme
fixed point theorems
convex structure
author_facet Lili Chen
Chaobo Li
Radoslaw Kaczmarek
Yanfeng Zhao
author_sort Lili Chen
title Several Fixed Point Theorems in Convex <i>b</i>-Metric Spaces and Applications
title_short Several Fixed Point Theorems in Convex <i>b</i>-Metric Spaces and Applications
title_full Several Fixed Point Theorems in Convex <i>b</i>-Metric Spaces and Applications
title_fullStr Several Fixed Point Theorems in Convex <i>b</i>-Metric Spaces and Applications
title_full_unstemmed Several Fixed Point Theorems in Convex <i>b</i>-Metric Spaces and Applications
title_sort several fixed point theorems in convex <i>b</i>-metric spaces and applications
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2020-02-01
description Our paper is devoted to indicating a way of generalizing Mann&#8217;s iteration algorithm and a series of fixed point results in the framework of <i>b</i>-metric spaces. First, the concept of a convex <i>b</i>-metric space by means of a convex structure is introduced and Mann&#8217;s iteration algorithm is extended to this space. Next, by the help of Mann&#8217;s iteration scheme, strong convergence theorems for two types of contraction mappings in convex <i>b</i>-metric spaces are obtained. Some examples supporting our main results are also presented. Moreover, the problem of the <i>T</i>-stability of Mann&#8217;s iteration procedure for the above mappings in complete convex <i>b</i>-metric spaces is considered. As an application, we apply our main result to approximating the solution of the Fredholm linear integral equation.
topic b-metric space
mann’s iteration scheme
fixed point theorems
convex structure
url https://www.mdpi.com/2227-7390/8/2/242
work_keys_str_mv AT lilichen severalfixedpointtheoremsinconvexibimetricspacesandapplications
AT chaoboli severalfixedpointtheoremsinconvexibimetricspacesandapplications
AT radoslawkaczmarek severalfixedpointtheoremsinconvexibimetricspacesandapplications
AT yanfengzhao severalfixedpointtheoremsinconvexibimetricspacesandapplications
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