Thakur's Iterative Scheme for Approximating Common Fixed Points to a Pair of Relatively Nonexpansive Mappings

In this work, we propose the three-step Takur iterative process associated with two mappings in the setting of Banach space. Using this Takur 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.

Automated summary

In this work, we propose a three-step Takur iterative process associated with two mappings in the setting of Banach space. We use this iteration to approximate a common fixed point for a pair of noncyclic, relatively nonexpansive mappings and support our main result with a numerical example. Additionally, we provide a stronger version of our main result using von Neumann sequences and give some corollaries on the convergence of common best proximity points in uniformly convex Banach space.