@article{Abbas2026, 
author = {Athar Abbas and Somayya Komal and Hafiz Fukhar-ud-din and Muhammad Aqeel Ahmad Khan and Muhammad Jabir Khan},
title = {A novel modified one-step iterative method for common fixed points of three nonexpansive mappings},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {12094-12107},
keywords = {modified one-step iteration, common fixed point approximation, Kadec-Klee property, condition (P), uniformly convex Banach spaces, convergence},
url = {https://www.sciopen.com/article/10.3934/math.2026496},
doi = {10.3934/math.2026496},
abstract = {This paper proposes a novel modified one-step iterative scheme for approximating common fixed points of three nonexpansive mappings in uniformly convex Banach spaces. The proposed scheme extends the classical one-step iteration associated with two mappings, which can be recovered as a particular case by an appropriate choice of the third mapping. Weak convergence of the generated sequence is established under both the Kadec-Klee property (KKP) and the Opial condition, while strong convergence is obtained by assuming a modified condition (B). Moreover, we introduce a new Condition (P) tailored for three mappings, which reduces to the well-known Condition (S) in the case of two mappings. The results presented here broaden and unify several existing contributions in the theory of common fixed point approximation.}
}