Fixed point theorems for the Mann's iteration scheme in convex graphical rectangular b-metric spaces. (3rd June 2021)

• Record Type: Journal Article
• Authors: Chen, Lili; Yang, Ni; Zhao, Yanfeng
• Is Part Of: Optimization. Volume 70:Number 5/6(2021)
• Page Start: 1359
• Page End: 1373
• Publication Date: 2021-06-03
• Subjects: Convex graphical rectangular b-metric spaces -- G-contraction mapping -- convex structure -- Mann's iterative algorithm; 47H09 -- 47H10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1887180
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we first introduce the concept of the convex graphical rectangular b -metric space ( G R b C M S ) by means of the convex structure. Moreover, the definitions of G -contraction mappings, G -quasi-contraction mappings, T -Mann sequences and TB -Mann sequences are presented in G R b C M S . Then we obtain strong convergence theorems for these mappings in G R b C M S under some suitable conditions. Furthermore, an example for supporting our main result is shown.