Approximating fixed points of non-self nonexpansive mappings in Banach spaces

Approximating common fixed points of finite family of asymptotically nonexpansive non-self mappings

“…Our results also extend the corresponding results of Shahzad [18] to the case of multistep iterative sequences with errors for a finite family of more general class of nonexpansive mappings.…”

Weak and Strong Convergence for Quasi-Nonexpansive Mappings in Banach Spaces

“…In this paper, we first show that the iteration {xn} defined by x n+1 = P ((1 − αn)xn + αnT P [βnT xn + (1 − βn)xn]) converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10].…”

Common Fixed Points of Two Nonexpansive Mappings by a Modified Faster Iteration Scheme

“…We note that (1.4) reduces to Mann iteration scheme (1.2) when T = I or S = I. The following Ishikawa type iteration scheme has been studied by various authors for common fixed points of two mappings, see for example [5], [9], [10], [15] and [17].…”