Location of the zeros of certain parametric families of functions of generalized Fresnel integral type

摘要

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.