Solvability of a system of integral equations of Volterra type in the Fréchet space lp loc(R+) via measure of noncompactness

Abstract

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.

Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem

“…Along of inequality (11) and applying (iv), the function Υ maps (B r 0 ) 2 intoB r 0 . Now, we shall prove the continuity of function Υ on (B r 0 ) 2 .…”

“…For more details on the theory of measure of noncompactness, its applications and its relations with nonlinear analysis we refer the reader to [8][9][10][11][12][13].…”

Measures of noncompactness and infinite systems of integral equations of Urysohn type in $L^\infty(\mathfrak{G})$

“…Heretofore, applying MNC approaches many articles have been extracted on the existence and behavior of solutions for nonlinear differential and integral equations. Some of these papers are [2,3,6,7,11,14].…”

On New Extensions of Darbo’s Fixed Point Theorem with Applications

“…This notion is also applied in studies of the existence of solutions of ODE and PDE problems, integral and integro-differential equations, etc. For more details, we refer the reader to [2][3][4][5][6]. In [7], the authors generalized the Darbo's fixed point theorem via the concept of the class of operators O( f ; .…”