Approximating Fixed Points of Operators Satisfying the (Bγ,μ) Condition.

Suppose C is any nonempty subset of a Banach space X. A mapping T : C → C is said to satisfy condition (B_γ,μ) if there exists μ ∈ [0, 1] and μ ∈ [0, 1/2 ] with 2μ ≤ γ such that for each two elements 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 research, we suggest some convergence results for these mappings under a up-to-date iterative process in a Banach space setting. Our results are new and improve some known results of the literature. [ABSTRACT FROM AUTHOR]