Equivalence of Certain Iteration Processes Obtained by Two New Classes of Operators

Mujahid Abbas, Rizwan Anjum and Vasile Berinde
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Mujahid Abbas: Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
Rizwan Anjum: Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan
Vasile Berinde: Department of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Victoriei 76, 430122 Baia Mare, Romania

Mathematics, 2021, vol. 9, issue 18, 1-15

Abstract: The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for such classes of mappings are equivalent. An application of the main results to solve split feasibility and variational inequality problems are also given.

Keywords: fixed point; Ishikawa iteration; Mann iteration; Krasnoselskij iteration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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