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.

The purpose of this article is to analyze the existence of solutions for a system of integral equations of Volterra type in the Fréchet space Lp loc(R+) and prove a fixed point theorem of Darbo-type in this space. The technique of measure of noncompactness by applying fixed point theorem is the main tool in carrying out our proof. Moreover, we present an example to show the efficiency of our results.

In this paper, we extend Darbo’s fixed point theorem via weak JS-contractions in a Banach space. Our results generalize and extend several well-known comparable results in the literature. The technique of measure of non-compactness is the main tool in carrying out our proof. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

In this paper, an extension of Darbo’s fixed point theorem via the concept of operators A(f;.) and θ-ω-contractions in a Banach space has been presented. We illustrate that some conditions of control functions ∂ and ω can be omitted where they applied previously in [Mohammadi et al., Mathematics, 2020, 8(4), 492]. As an application, we study the existence of solutions for a system of fractional integral equations. Finally, to support the effectiveness of our results, we present an example.

In this paper, by applying the behavior of measure of noncompactness in L^∞( $\mathbb{R}$ⁿ), we study the existence of solutions of an infinite system of integral equations in the space L^∞( $\mathbb{R}$ⁿ). Finally, an example is included to show the usefulness of the outcome.