Iterative approximations of fixed points for operators satisfying (<em>B<sub>γ,μ</sub></em>) condition



	*Iterative approximations of fixed points for operators satisfying (B_γ,μ) condition*


	Fixed Point Theory, Volume 22, No. 2, 2021, 887-898, July 1st, 2021 DOI: 10.24193/fpt-ro.2021.2.58 Authors: Kifayat Ullah and Junaid Ahmad Abstract: Let C be a nonempty subset of a Banach space X. A mapping T : C → C is said to satisfy(B_γ,μ) condition if there exists γ ∈ [0,1] and μ ∈ [0, ½] satisfying 2μ ≤ γ such that for each x,y ∈ C, γ‖x-Tx‖≤‖x-y‖+μ‖y-Ty‖ implies ‖Tx-Ty‖≤(1-γ)‖x-y‖+μ(‖x-Ty‖+‖y-Tx‖). In this paper, we obtain some convergence theorems for such mappings using M iterative process in uniformly convex Banach space setting. Our results extend and improve many results in the literature. Key Words and Phrases: Condition (B_γ,μ, weak convergence, strong convergence, M iteration, Banach space. 2010 Mathematics Subject Classification: 47H05, 47H09, 47H10. Published on-line: July 1st, 2021. Abstract pdf Fulltext pdf Back to volume's table of contents