Abstract In this paper, two parametric families of functions, the so-called Complementary Fresnel Integral and of the Lommel type, which are of generalized Fresnel integral type, are considered. We review the problems of existence and uniqueness of their zeros in certain determined intervals, called location intervals, which improve previous results of other authors. For the approximation error obtained, bounds, monotonicity as well as the asymptotic behavior are analyzed. The study uses results from the theory of fixed point of real functions, introducing the concept of “fixed point sequential problem” (FPSP) and the properties of certain special functions. On the other hand some special inequalities for parametric functions are derived and used all along the proofs of the main results.

中文翻译：

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广义菲涅耳积分型函数的某些参数族的零点位置

摘要 本文考虑了广义菲涅尔积分类型的两个参数函数族，即所谓的互补菲涅耳积分和洛梅尔类型。我们回顾了在某些确定的区间（称为位置区间）中零点的存在性和唯一性的问题，这改进了其他作者之前的结果。对于得到的近似误差，分析了边界、单调性以及渐近行为。该研究利用实函数不动点理论的结果，引入了“不动点序列问题”（FPSP）的概念和某些特殊函数的性质。另一方面，推导出参数函数的一些特殊不等式，并在主要结果的证明中使用。