On the Convergence and Stability of AP Iteration Process in CAT(0) Spaces

Abstract

In this paper, we use the AP iteration method in the context of CAT(0) space to approximate invariant points for contraction maps. We also prove that our iteration process for contraction map is faster than the leading Picard-S iteration process to demonstrate the proposed algorithm’s convergence behaviour. To support the analytic proofs, numerical examples are given. Furthermore, we demonstarte that the AP iteration method is T-stable.

2010 AMS Subject Classification: 47H10, 54H25, 54E50.