Strong convergence of Halpern's type iteration for <em>α</em>-nonexpansive semigroup in Banach spaces and CAT(0) spaces



	Strong convergence of Halpern's type iteration for α-nonexpansive semigroup in Banach spaces and CAT(0) spaces


	Fixed Point Theory, Volume 25, No. 1, 2024, 271-288, February 1st, 2024 DOI: 10.24193/fpt-ro.2024.1.17 Authors: Dolapo Muhammed Oyetunbi and Abdul Rahim Khan Abstract: In this paper, we establish strong convergence of the Halpern's type iteration for a semigroup of α-nonexpansive mappings in Banach spaces. Using the concept of quasilinearization, we extend this result to CAT(0) spaces, an important subclass of metric spaces. Our work generalizes and complements several comparable results existing in the literature. Key Words and Phrases: Semigroup, α-nonexpansive mapping, common fixed point, Banach space, CAT(0) space. 2010 Mathematics Subject Classification: 49J40, 47H05, 65J15, 47H10, 47H09, 47J25. Published on-line: February 1st, 2024. Fulltext pdf Back to volume's table of contents