Abstract
We study the existence of solutions of a nonlinear Volterra integral equation in the spaceL1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.
Highlights
We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0, +∞)
With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations
We present an existence result for the functional integral equation x (t) = g (t, x (t), x (ψ1 (t)))
Summary
We present an existence result for the functional integral equation x (t) = g (t, x (t) , x (ψ1 (t))). The main tool used in our research is a measure of weak noncompactness given by Banas and Knab [3] to find a special subset of L1[0, ∞) and by applying the Krasnoselskii’s fixed point theorem on this set. Let us mention that the theory of functional integral equations has many useful applications in describing numerous events and problems of the real world. Notations, and auxiliary facts are presented in Section 2; in Section 3, we will introduce the main tools: measure of weak noncompactness and Krasnoselskii’s fixed point theorem.
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