Fixed Point Theorems for Weak Contractions via λ-Iteration in Cone b-Metric Banach Spaces with Applications

Elvin Rada

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.

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Pan-Amer. J. Math. 4 (2025), 18
DOI: https://doi.org/10.28919/cpr-pajm/4-18
This article was published on November 11, 2025 by Mathyze, under a Creative Commons Attribution 4.0 International License.