On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals

Abstract

We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration.

Fixed Point Approximation Using Unified Iteration Scheme for Asymptotically Nonexpansive Mappings in Cat(0) Spaces

“…If C be a complete CAT (0) space, then A({m n }) contains exactly one point (see Proposition 5 of [6]).…”