ABSTRACT
This chapter discusses some elementary applications of fixed point theorems in root finding, establishing the existence and uniqueness of solutions of systems of linear algebraic equation, steady states of Markov processes, integral equations, initial value and boundary value problems. It also discusses periodic and impulsive boundary value problems, equilibrium of difference equations and periodic solutions of cyclic systems. A stochastic process with a finite number of states such that the state of system at any stage depends only on its previous stage is called a Markov process. The chapter considers the Cauchy initial value problem. The study of nonlinear difference equations, which plays an important role in modelling problems in economics, biology, ecology, genetics, psychology, sociology, probability theory and other is a topic of great interest. The difference equations of order greater than one are studied by many authors.
