On the stability and convergence of Mann iteration process in convex A- metric spaces

Publication date: 15 January 2021

Abstract: In this paper, firstly, we introduce the concept of convexity in A-metric spaces and show that Mann iteration process converges to the unique fixed point of Zamfirescu type contractions in this newly defined convex A-metric space. Secondly, we define the concept of stability in convex A-metric spaces and establish stability result for the Mann iteration process considered in such spaces. Our results carry some well-known results from the literature to convex A-metric spaces.

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

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