The form of the unit iterative root f(x)(X∈R) is generalized , that is, the form of the unit iterative root of linear transformation in R~n is discussed.

In this paper it was obtained a necessary and sufficient condition for m-piece monotone continuous self-map F of the iterval I=[0,1]with N(F)=N(F2) to have the n-fold iterative solutions.

A necessary and sufficient conditionf of expanding Markov surjective self maps with iterative solutions is obtained.

In this paper,we discuss iterative solutions of all N type of functions (briefly: increase-decrease-increase type of function)on the interval I=[0, 1].

Algorithms for Iterative Roots and Iterative Equations and Their Stability;

Nonexistence of iterative roots of PM functions

The existence of decreasing roots of the conjugate function φ(f(x))=g(φ(x)) is discussed when f and g are decreasing,and the existence of iterative roots of one kind of functions which have two non-monotone points is studied.

First,we constructed a pair of appropriate upper and lower solutions,and then we proved the existence of the traveling wave solutions between two equilibria of the system by using the monotone iteration approach.

This paper is devoted to investigate a kind of lattice Nicholson s blowflies model with delay,and prove the existence of traveling wavefronts by upper-lower solution and monotone iteration technique.

It is shown that the system exist monotone traveling wave solutions by using monotone iteration with upper and lower solutions provided wave speed satisfies some conditions.

The method of upper and lower solutions and the monotone iterative technique are used.

By using cone theorem and monotone iterative method, the mixed monotone condition in A(x,y)+Mx in Banach spaces is extended.

It obtains the existence results by using the monotone iterative method of lower and upper solutions and improves the results.