Equivalence results for implicit Jungck–Kirk type iterations

Abstract

We show that the implicit Jungck–Kirk-multistep, implicit Jungck–Kirk–Noor, implicit Jungck–Kirk–Ishikawa, and implicit Jungck–Kirk–Mann iteration schemes are equivalently used to approximate the common fixed points of a pair of weakly compatible generalized contractive-like operators defined on normed linear spaces. Our results contribute to the existing results on the equivalence of fixed point iteration schemes by extending them to pairs of maps. An example to show the applicability of the main results is included.