On the Equivalence of Stochastic Fixed Point Iterations for Generalized φ-Contractive-Like Operators

Abstract

We present the equivalence of some stochastic fixed point iterative algorithms by proving the equivalence between the convergence of random implicit Jungck-Kirk-multistep, random implicit Jungck-Kirk-Noor, random implicit Jungck-Kirk-Ishikawa, and random implicit Jungck-Kirk-Mann iterative algorithms for generalized -contractive-like random operators defined on separable Banach spaces.

The equivalence between the (S,T)− stabilities of Jungck-type iterative schemes

“…The equivalence of convergence of various iterative schemes of Jungck-type have been extensively studied in literature, notable authors whose contributions are of colossal value are [4,5,10].…”

Random Common Fixed Point Theorems for Two Pairs of Nonlinear Contractive Maps in Polish Spaces

“…Some classical fixed point theorems in different abstract spaces are proved in the context of random fixed point theory (see; Akewe et al [1] , Rashwan and Albaqeri [2], Hans [3] and Nieto et al [4]). The common fixed point of two pairs of weakly compatible mappings satisfying certain contractive conditions in G-partial metric spaces without assuming the continuity of any of the maps involved was proved by Eke and Akinlabi [8].…”