The Study of the Solvability of Infinite Systems of Integral Equations via Measures of Noncompactness

Abstract

The paper is devoted to investigate the existence of solutions of infinite systems of nonlinear quadratic integral equations of Volterra type. We look for solutions of those infinite systems of integral equations which are defined, continuous and bounded on the real half-axis and take real values. In our considerations the basic role will be played by the technique of measures of noncompactness defined in the space of functions defined, continuous and bounded on the real half-axis with values in the sequence space $l_{\infty }$ consisting of real sequences equipped with the standard supremum norm. We are going to prove an existence result which generalizes all recently obtained results for infinite systems of integral equations. An example illustrating the obtained result will be included.

Keywords:

• Space of real functions defined
• continuous and bounded on the real half-axis
• sequence space
• measure of noncompactness
• fixed point theorem of Darbo type
• infinite system of integral equations

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 47H08
• Secondary: 45G10