TITLE:
On the Equivalence of Implicit Kirk-Type Fixed Point Iteration Schemes for a General Class of Maps
AUTHORS:
Alfred Olufemi Bosede, Hudson Akewe, Omolara Fatimah Bakre, Ashiribo Senapon Wusu
KEYWORDS:
Implicit Kirk-Multistep, Implicit Kirk-Mann Iterations, Strong Convergence, Equivalence, General Class of Maps
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.1,
January
17,
2019
ABSTRACT: In this paper, a modified
implicit Kirk-multistep iteration scheme and a strong convergence result for a
general class of maps in a normed linear space was established. It was also
shown that the convergence of this iteration scheme is equivalent to the
convergency of some other implicit Kirk-type iteration (implicit Kirk-Noor,
implicit Kirk-Ishikawa and implicit Kirk-Mann iterations) for the same class of
maps. Some numerical examples were considered to show that the equivalence of
convergence results to the fixed point is true. The results unify most
equivalence results in literature.