Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

中文翻译：

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实半轴上积分方程的无限系统的可解性

摘要 本文的目的是研究实半轴上非线性积分方程的无穷大系统的可解性。考虑将位于函数序列的空间中，该空间以半轴的每个点为界。研究中使用的主要工具是与在实半轴上定义、连续和有界函数空间中的非紧凑性度量相关的技术，空间 l∞ 中的值由具有标准最高范数的实有界序列组成。在我们的考虑中的重要作用是，我们将使用基于上述序列空间 l∞ 中的非紧凑性度量构建的非紧凑性度量。将包括一个说明我们结果的示例。