In this paper, we extend Darbo's fixed point theorem in Banach space via the concept of the class of operators O(f;.) and obtain a tripled fixed point theorem. The main tool applied in our investigation is the technique of measures of noncompactness. Finally, as an application of our obtained results, we analyze the existence of solutions for a system of integral equations. [ABSTRACT FROM AUTHOR]
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. [ABSTRACT FROM AUTHOR]