On some common fixed point results for two infinite families of uniformly L-Lipschitzian total asymptotically quasi-nonexpansive mappings

• Published in: Fixed point theory and algorithms for sciences and engineering Vol. 2024; no. 1; pp. 12 - 16
• Main Authors: Nuntadilok, Buraskorn, Kingkam, Pitchaya, Nantadilok, Jamnian, Samanmit, Khanitin
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.08.2024; Springer Nature B.V; SpringerOpen
• Subjects: Algorithms; Analysis; Applications of Mathematics; Asymptotically quasi-nonexpansive map; CAT space; Common fixed point; Convergence; Differential Geometry; Hyperbolic space; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; Metric Fixed Point Theory and Its Applications; Topology; Total asymptotically nonexpansive mappings; Δ-Convergence; Total asymptotically nonexpansive mappings; Asymptotically quasi-nonexpansive map; Δ-Convergence; Common fixed point; CAT; CAT space; space; Hyperbolic space
• ISSN: 2730-5422; 2730-5422
• DOI: 10.1186/s13663-024-00768-z

In this manuscript, we introduce a new class of uniformly L -Lipschitzian and total asymptotically quasi-nonexpansive mappings, which is significantly more general than many known nonexpansive mappings that appeared before. We establish some convergence and Δ-convergence theorems for two infinite families of such mappings in the setting of CAT( κ ) spaces. Our results refine, generalize, and improve several corresponding results in the existing literature.