Accelerated inertial Jungck iterative scheme for Jungck generalised pseudocontractive and S-Lipschitzian mappings in Hilbert spaces
DOI:
https://doi.org/10.53704/Keywords:
Jungck generalized pseudocontraction; S-Lipschitzian mapping; inertial iteration; Jungck iterative process; strong convergence; common fixed point.Abstract
In this paper, we introduce an accelerated inertial Jungck iterative framework for approximating common fixed points of Jungck generalised pseudocontractive and -Lipschitzian mappings in real Hilbert spaces. The proposed iteration combines inertial extrapolation, predictor–corrector approximation and viscosity-type stabilisation to improve the convergence behaviour of the classical Jungck–Schaefer and Jungck–Kirk–Mann iterative schemes. Under suitable assumptions on the pair of commuting mappings and admissible control sequences, we establish boundedness, asymptotic regularity, weak convergence and strong convergence of the generated sequence to a common fixed point. Furthermore, we obtain an asymptotic error-majorant comparison theorem for the accelerated core of the proposed method under explicit uniform control conditions. Our results extend and improve several related results in the literature, including those of Olatinwo and Omidire (2021) and related Jungck iterative frameworks.
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Copyright (c) 2026 Olaoluwa Omidire, Babatunde Ishola, Dare Ariyo
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain copyright of their work, with first publication rights granted to Fountain Journal of Natural and Applied Sciences. Articles in FUJNAS are published on the Creative Commons Attribution 4.0 International license (CC BY 4.0).
