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In this paper we extend Darbo's fixed point theorem in Banach spaces and obtain a tripled fixed point theorem. The technique of measure of noncompactness is the main tool in carrying out our proof. Finally, as an application of our results, we analyze the existence of solutions for a system of neutral differential 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 L p 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 article, we prove some Darbo's type fixed point theorems associated with measure of noncompactness via the concept of operators A(f ; .) and weakly J S-contractive condition in Banach space. Moreover, as an application of our results, we study the existence of solutions for a system of differential equations. Finally, we present an example to support the effectiveness of our results. Keywords Fixed point theorem • Measure of noncompactness • Condensing operator • Differential equation Mathematics Subject Classification Primary 47H08 • 47H10 1 Introduction Fixed point theory is one of the most effective and applicable tools used in analysis to study the existence of solutions for a system of differential equations. Kuratowski (1930) in 1930, opened up a new direction of research with the presentation of the notion of a measure of noncompactness (MNC). Darbo's fixed point theorem (Darbo 1955) is an important application Communicated by Carlos Conca.