The purpose of this research is to connect fixed point methods with certain third-order boundary value problems in new and interesting ways. Our strategy involves an analysis the problem under consideration within closed bounded sets. We develop sufficient conditions which associated mappings will be contractive invariant these sets, generates advances concerning existence, uniqueness approxima...

This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and absence of stationary distributions are established and uniqueness is proved. Also, convergence rates to the stationary distribution are given. Linear equations w...

In this article, we study a class of mixed monotone operators with perturbations. Using a monotone iterative technique and the properties of cones, we show the existence and uniqueness for fixed points for such operators. As applications, we prove the existence and uniqueness of positive solutions for nonlinear integral equations of second-order on time scales. In particular, we do not assume t...