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Open AccessArticle

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

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College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
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Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China
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Poznań, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 242; https://doi.org/10.3390/math8020242
Received: 3 January 2020 / Revised: 8 February 2020 / Accepted: 10 February 2020 / Published: 14 February 2020
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with 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 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. View Full-Text
Keywords: b-metric space; Mann’s iteration scheme; fixed point theorems; convex structure b-metric space; Mann’s iteration scheme; fixed point theorems; convex structure
MDPI and ACS Style

Chen, L.; Li, C.; Kaczmarek, R.; Zhao, Y. Several Fixed Point Theorems in Convex b-Metric Spaces and Applications. Mathematics 2020, 8, 242.

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