"In this article, applying the concept of measure of noncompactness, some fixed point theorems in the Fréchet space $L^\infty(\mathfrak{G})$ (where $\mathfrak{G}\subseteq \mathbb{R}^{\omega}$) have been proved. We handle our obtained consequences to inquiry the existence of solutions for infinite systems of Urysohn type integral equations. Our results extend some famous related results in the literature. Finally, to indicate the effectiveness of our results we present a genuine example."
The aim of this paper is to investigate the solvability of infinite systems of nonlinear functional integral equations of [Formula: see text]-variables in [Formula: see text] by using the Hausdorff measure of noncompactness with the help of Meir–Keeler condensing operators. We also provide an illustrative example in support of our existence theorems.
In this paper, an extension of Darbo’s fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. 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, we prove theorems on the existence of solutions in Lp(R+), 1 ? p < ?, for some functional integral equations. The basic tool used in the
proof is the fixed point theorem due to Darbo with respect to so called
measure of noncompactness. The obtained results generalize and extend
several ones obtained earlier in many papers and monographs. An example
which shows the applicability of our results is also included.
We propose a new notion of contraction mappings for two class of functions
involving measure of noncompactness in Banach space. In this regard we
present some theory and results on the existence of tripled fixed points and
some basic Darbo?s type fixed points for a class of operators in Banach
spaces. Also as an application we discuss the existence of solutions for a
general system of nonlinear functional integral equations which satisfy in
new certain conditions. Further we give an example to verify the
effectiveness and applicability of our results.
The purpose of this article is to analyze the existence of solutions for a
system of integral equations of Volterra type in the Fr?chet 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.
Measures of noncompactness and infinite systems of integral equations of Urysohn type in $L^\infty(\mathfrak{G})$
