Ishikawa-Mann-Fibonacci Best Proximity Points for Cyclic Relatively Nonexpansive Mappings

Abstract

We study best proximity point convergence for cyclic relatively nonexpansive mappings in uniformly convex Banach spaces. We analyze two Mann-type iterations: the n-powered scheme and its Fibonacci-accelerated variant. Under suitable conditions, we establish strong and weak convergence theorems. Our main result shows that the n-powered iteration converges strongly to a best proximity point, while the Fibonacci variant achieves doubly exponential convergence. An application to optimal traffic signal timing is provided.