Convergence, stability and data dependence results for contraction and nonexpansive mappings by a new four step algorithm

Subject Areas : Fixed point theory

U. E. Udofia ¹ (Department of Mathematics, Akwa Ibom state University, Ikot Akpaden, Mkpat Enin, Nigeria)
D. Igbokwe ² (Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria)

Received: 2021-09-02 Accepted : 2021-12-18 Published : 2021-12-19

Keywords: Stability, Nonexpansive mapping, Banach space, contraction mapping, Data Dependence,

Abstract :

Here we show that the UI-iteration scheme (Udofia and Igbokwe, [24]) can be used to approximate the fixed points of contraction and nonexpansive mappings. we prove a strong and weak convergence of the iteration scheme to the fixed point of contraction and nonexpansive mappings. We also prove that the scheme is Γ-stable and data dependent. Analytically and with numerical example we show that the UI-iteration scheme has a faster rate of convergence for contraction and nonexpansive mappings than some well known existing iteration schemes in literature. Finally, we apply the UI-iteration scheme to find the solution of constrained convex minimization problem.

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