2022/01/07 by Mohamed Rossafi, Rossafi, Mohamed, Abdelkarim Kari +1
Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #General Topology (math.GN) #Metric Geometry (math.MG) #Primary 47H10 #Secondary 54H25
paper · pdf · doi:10.48550/arxiv.2201.05691
openalex publication_date 2022/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce an extension of rectangular metric spaces called controlled rectangular metric spaces, by changing the rectangular inequality as follows: d(x, y)≤α(x, u)d(x, u)+α(u, v)d(u, v)+α(v, y)d(v, y), for all distinct x, y, u, v∈ X with the function α: X× X→[1,∞[. We also establish some fixed point theorems for self-mappings defined on such spaces. Our main results extends and improves many results existing in the literature. Moreover, an illustrative example is presented to support the obtained results.