Abstract
In this article, we attempt to provide a more general method based on
Petryshyn’s fixed-point theorem to ensure the existence of solutions to
implicit functional equations. These implicit functional equations
include fractional, non-fractional, (fractional) stochastic integral
equations, etc., and any combination of them in C( I).
Some results regarding the existence of fixed points in implicit
functional integral equations will be reviewed in the literature. We
show that this general result unifies and improves many of the main
results in the literature. To illustrate that our approach is more
general than other methods, we present some concrete examples. Also, we
apply our method to create new functional equations in practice and
check the existence of solutions.