The paper deals with a Volterra integral equation with delay. In order to apply the w-weak generalized contraction theorem for the study of existence and uniqueness of solutions, we rewrite the equation as a fixed point problem. The assumptions take into account the support of w-distance and the complexity of the delay equation. Gronwall-type theorem and comparison theorem are also discussed using a weak Picard operator technique. In the end, an example is provided to support our results.

中文翻译：

---

关于具有延迟的 Volterra 积分方程，通过 w-Distances

该论文涉及一个带延迟的 Volterra 积分方程。为了应用 w-弱广义收缩定理来研究解的存在唯一性，我们将方程重写为不动点问题。这些假设考虑了 w-distance 的支持和延迟方程的复杂性。还使用弱 Picard 算子技术讨论了 Gronwall 型定理和比较定理。最后，提供了一个例子来支持我们的结果。