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

Lili Chen, Chaobo Li, Radoslaw Kaczmarek and Yanfeng Zhao
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Lili Chen: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Chaobo Li: Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China
Radoslaw Kaczmarek: Poznań, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland
Yanfeng Zhao: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2020, vol. 8, issue 2, 1-16

Abstract: 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.

Keywords: b-metric space; Mann’s iteration scheme; fixed point theorems; convex structure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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