In this work, we propose the three‐step Thakur iterative process associated with two mappings in the setting of Banach space. Using this Thakur iteration, we approximate a common fixed point for a pair of noncyclic, relatively nonexpansive mappings. And we support our main result with a numerical example. Also, we give a stronger version of our main result by using von Neumann sequences. Finally, we provide some corollaries on the convergence of common best proximity points in uniformly convex Banach space.

The study of symmetry is a major tool in the nonlinear analysis. The symmetricity of distance function in a metric space plays important role in proving the existence of a fixed point for a self mapping. In this work, we approximate a fixed point of noncyclic relatively nonexpansive mappings by using a three-step Thakur iterative scheme in uniformly convex Banach spaces. We also provide a numerical example where the Thakur iterative scheme is faster than some well known iterative schemes such as Picard, Mann, and Ishikawa iteration. Finally, we provide a stronger version of our proposed theorem via von Neumann sequences.