On (˛, )-Relaxed Polygonal Metric Spaces and Fixed Point Results
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Bessem Samet [1]
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[1] King Saud University
King Saud University
Arabia Saudí
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- Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
- Idioma: inglés
- Enlaces
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Resumen
We introduce the notion of(α, ν)-relaxed polygonal metric spaces, where α > 0 and ν :
[0,∞) → [0,∞) is a function satisfying certain conditions. This notion generalizes the concept of s-relaxedp metric spaces proposed by Fagin et al. (SIAM J Discrete Math 17(1): 134–160, 2003). The originality of the introduced notion is justified by examples of (α, ν)-relaxed polygonal metric spaces that are not s-relaxedp metric spaces. We establish several properties of (α, ν)-relaxed polygonal metric spaces. In particular, we introduce the concept of (α, ν)-metric bounded distance, and show that, if δ : Z × Z → [0,∞) is symmetric, then δ is a (α, ν)-relaxed polygonal metric, if and only if δ is a (α, ν)-metric bounded distance. We next define the convergence of sequences, Cauchy sequences, and completeness. We also establish some fixed point results in (α, ν)-relaxed polygonal metric spaces. Namely, we extend the Banach contraction principle and the Kannan fixed point theorem from metric spaces to (α, ν)- relaxed polygonal metric spaces. The novelty of our fixed point results are supported by examples in which the standard Banach and Kannan fixed point theorems are not applicable.
