2024/04/08 by H. Baranwal, Baranwal, H., Asha Chand +1
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #Economic theories and models #FOS: Mathematics #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2406.15368
openalex publication_date 2024/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cyclic contractions generalize the usual contractivities in metric spaces and b-MSs. In this paper, we enhance several fixed point theorems related to cyclic (i) Banach self-maps, (ii) Chatterjea contractivities, (iii) Kannan self-mappings, (iv) Ćirić and Hardy-Rogers, and (v) Reich contractions including local versions in b-metric spaces while also delineating the associated dynamics. Especially noteworthy is the expansion of the results concerning both fixed and periodic points, which are substantiated across a wider spectrum of ratio values for the aforementioned cyclic contractions within this class of spaces. Additionally, the convergence of Picard iterations towards the fixed point is rigorously established.