Research article
Fixed Point Theorems for Weak Contractions via λ-Iteration in Cone b-Metric Banach Spaces with Applications
Abstract
We develop fixed point results for weakly contractive mappings in complete cone b-metric Banach spaces. Using a generalized λ-averaged iteration, we derive convergence, uniqueness, and stability under summable perturbations. We also establish an ordered version and give fully proved applications to Hammerstein integral equations and a matrix Lyapunov-type equation. Our results unify and extend Berinde-type weak contractions from (classical) b-metric and cone metric settings to cone b-metric Banach spaces, and clarify optimal choices of λ ensuring geometric convergence.
How to cite
E. Rada, Fixed Point Theorems for Weak Contractions via λ-Iteration in Cone b-Metric Banach Spaces with Applications, Pan-Amer. J. Math. 4 (2025), 18. https://doi.org/10.28919/cpr-pajm/4-18
BibTeX
@article{Rada2025,
author = {Rada, Elvin},
title = {Fixed Point Theorems for Weak Contractions via λ-Iteration in Cone b-Metric Banach Spaces with Applications},
journal = {Pan-Amer. J. Math.},
volume = {4},
year = {2025},
pages = {18},
doi = {10.28919/cpr-pajm/4-18}
}