Several Fixed Point Theorems in Convex b-Metric Spaces and Applications

Our paper is devoted to indicating a way of generalizing Mann’s iteration algorithm and a series of fixed point results in the framework of b-metric spaces. First, the concept of a convex b-metric space by means of a convex structure is introduced and Mann’s iteration algorithm is extended to this s...

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Published inMathematics (Basel) Vol. 8; no. 2; p. 242
Main Authors Chen, Lili, Li, Chaobo, Kaczmarek, Radoslaw, Zhao, Yanfeng
Format Journal Article
LanguageEnglish
Published MDPI AG 01.02.2020
Subjects
b-metric space
convex structure
fixed point theorems
mann’s iteration scheme
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Summary:Our paper is devoted to indicating a way of generalizing Mann’s iteration algorithm and a series of fixed point results in the framework of b-metric spaces. First, the concept of a convex b-metric space by means of a convex structure is introduced and Mann’s iteration algorithm is extended to this space. Next, by the help of Mann’s iteration scheme, strong convergence theorems for two types of contraction mappings in convex b-metric spaces are obtained. Some examples supporting our main results are also presented. Moreover, the problem of the T-stability of Mann’s iteration procedure for the above mappings in complete convex b-metric spaces is considered. As an application, we apply our main result to approximating the solution of the Fredholm linear integral equation.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8020242