The Fixed Point Theorems With Applications Of Several Classes Of Non-linear Operators

In this text we study the existence of fixed points of some non-linear operators by using of cone and partial order method(convex-power condensing operator; non-linear operator without mixed monotone; systems of equations with mixed monotone), and set up some new results.In Chapter 1, we introduce some basic knowledge that should be utilized in the article.In Chapter 2, in the basic of convex-power condensing operator which is introduced in paper[29], we continue to study the fixed point problem of increasing operator and convex-power condensing operator, and obtain the fixed point theorems, The results obtained in this chapter improve and generalize some known results of increasing operator.In Chapter 3, we discuss the fixed point theorems of non-linear operator on the basic of changing and expanding the conditions in paper[18] and [19], in which the operators areα-concave convex. The results generalize the theorems of paper[1] and [21] .In Chapter 4, we investigate the existence and uniqueness theorems of solutions for the systems of some mixed monotone operator equations in the basic of the fixed point theorems of mixed monotone operator, and we draw to some theorems which expand the application of mixed monotone operator. The results obtained are applied to study the solution of non-linear integral equations.