Abstract
In this article, the recently introduced iterative scheme of Hassan et al. (Math. Probl. Eng. 2020) is re-analyzed with the connection of Reich–Suzuki type nonexpansive (RSTN) maps. Under mild conditions, some important weak and strong convergence results in the context of uniformly convex Banach spaces are provided. To support the main outcome of the paper, we provide a numerical example and show that this example properly exceeds the class of Suzuki type nonexpansive (STN) maps. It has been shown that the Hassan et al. iterative scheme of this example is more useful than the many other iterative schemes. We provide an application of our main results to solve split feasibility problems in the setting of RSTN maps. The presented outcome is new and compliments the corresponding results of the current literature.
Highlights
Introduction and PreliminariesDifferent kinds of numerical schemes, especially iteration schemes were successfully applied for finding the solutions of many different kinds of functional, differential and integral operators
Suppose a selfmap T : D → D is Reich–Suzuki type nonexpansive (RSTN) endowed with FT = ∅ and {rm} is a sequence obtained from the iterative scheme (8)
Suppose a selfmap T : D → D is RSTN and {rm} is a sequence obtained from the iterative scheme (8)
Summary
Introduction and PreliminariesDifferent kinds of numerical schemes, especially iteration schemes were successfully applied for finding the solutions of many different kinds of functional, differential and integral operators (see e.g., [1,2,3] and others). It has been known for many years that every nonexpansive selfmap admits a fixed point (which may not be unique) when one considers M being a uniformly convex Banach space (UCBS) and the set D closed convex and bounded (cf [6,7,8] and others).
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