On (˛, )-Relaxed Polygonal Metric Spaces and Fixed Point Results

• Bessem Samet ^[1]
  1. [1] King Saud University

     King Saud University

     Arabia Saudí

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• 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.

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