Abstract
The purpose of this paper is to introduce the random Jungck–Mann-type and the random Jungck–Ishikawa-type iterative processes. We prove some convergence and stability results for these random iterative processes for certain random operators. Furthermore, we apply our results to study random non-linear integral equation of the Hammerstein type. Our results generalize, extend and unify several well-known deterministic results in the literature. Moreover, our results generalize recent results of Okeke and Abbas and Okeke and Kim .
Highlights
Real-world problems are embedded with uncertainties and ambiguities
We introduce the random Jungck–Mann-type and the random Jungck–Ishikawa-type iterative processes
We prove the existence of a solution of a random non-linear integral equation of the Hammerstein type in a Banach space
Summary
Probabilistic functional analysis has attracted the attention of several well-known mathematicians due to its applications in pure mathematics and applied sciences. We prove the existence of a solution of a random non-linear integral equation of the Hammerstein type in a Banach space
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