Existence and approximating of common best proximity points of relatively nonexpansive mappings via Ishikawa iteration method



	Existence and approximating of common best proximity points of relatively nonexpansive mappings via Ishikawa iteration method


	Fixed Point Theory, Volume 24, No. 2, 2023, 595-610, June 15th, 2023 DOI: 10.24193/fpt-ro.2023.2.09 Authors: Moosa Gabeleh, Jack T. Markin and Vladimir Rakočevć Abstract: In this article, we study the existence of a common best proximity points for a finite class of cyclic relatively nonexpansive mappings in the setting of Busemann convex spaces. In this way, we extend the main results given in Eldred and Raj (2009) [A.A. Eldred, V.S. Raj, On common best proximity pair theorems, Acta Sci. Math. (Szeged), 75, 707-721] for relatively nonexpansive mappings in Banach spaces to more general metric spaces. We then present a strong convergence theorem of a common best proximity point for a pair of cyclic mappings in uniformly convex Banach spaces by using the Ishikawa iterative process. Key Words and Phrases: Best proximity point, fixed point, cyclic relatively nonexpansive, uniformly convex Banach space, iterative sequence. 2010 Mathematics Subject Classification: 47H09, 47H10, 90C48, 46B20. Published on-line: June 15th, 2023. Fulltext pdf Back to volume's table of contents