Integral Equations,?ε-Fixed Points, Fixed Point Regions, Linear Approximations, and a Family of Kernels

摘要

We study a nonlinear Volterra integral equation by first transforming it into an equivalent equation with kernel depending on an (arbitrary) positive number J.The notion of “ε-nearly fixed point” is introduced and a family of resolvent kernels along with a family of corresponding mappings are considered.A part of the paper is devoted to finding a region in which all possible solutions of the equation must reside, yet properties of the family of the resolvents are given.An extensive discussion containing an illustrative example is provided.