Convexity in G-metric spaces and approximation of fixed points by Mann iterative process

Document Type : Research Paper


1 Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, 25240, Turkey

2 Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar


In this paper, we first define the concept of convexity in G-metric spaces. We then use Mann iterative process in this newly defined convex G-metric space to prove some convergence results for some classes of mappings. In this way, we can extend several existence results to those approximating fixed points. Our results are just new in the setting.