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On the Equivalence of Implicit Kirk-Type Fixed Point Iteration Schemes for a General Class of Maps

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Document pages: 15 pages

Abstract: In this paper, a modifiedimplicit Kirk-multistep iteration scheme and a strong convergence result for ageneral class of maps in a normed linear space was established. It was alsoshown that the convergence of this iteration scheme is equivalent to theconvergency of some other implicit Kirk-type iteration (implicit Kirk-Noor,implicit Kirk-Ishikawa and implicit Kirk-Mann iterations) for the same class ofmaps. Some numerical examples were considered to show that the equivalence ofconvergence results to the fixed point is true. The results unify mostequivalence results in literature.

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