In this paper, we investigate the convergence of approximate solutions for a class of first-order integro-differential equations with antiperiodic boundary value conditions. By introducing the definitions of the coupled lower and upper solutions which are different from the former ones and establishing some new comparison principles, the results of the existence and uniqueness of solutions of the problem are given. Finally, we obtain the uniform and rapid convergence of the iterative sequences of approximate solutions via the coupled lower and upper solutions and quasilinearization method. In addition, an example is given to illustrate the feasibility of the method.

中文翻译：

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一阶积分微分方程反周期边值问题的收敛性

在本文中，我们研究了一类具有反周期边值条件的一阶积分-微分方程的近似解的收敛性。通过介绍上下耦合解的定义，并建立一些新的比较原理，给出了问题解的存在性和唯一性的结果。最后，通过耦合上下解和拟线性化方法，获得了近似解的迭代序列的一致且快速收敛。另外，通过实例说明了该方法的可行性。