Fixed Point Theorems For Several Kinds Of Nonlinear Operators

In this article, by using the cone theory, the non-symmetric iterative method andpartial ordering method, the existence and uniqueness of solutions for a class of systemsof decreasing operators in the Banach space, and the fixed point theorems for thecontractive mappings and the expanding mappings in the cone metric space are discussed.The main contents of this paper are as follows:In the first chapter, the research background and significance and the work of thisarticle are showed.In the second chapter, by using the non-symmetric iterative method, the existenceand uniqueness of fixed point for a kind of systems of decreasing operators. And theiterative sequences which converge to solution of operators equations and the errorestimates are obtained.At the same time, in the continuous conditions, the random fixed point of somerandom anti-mixed monotone operator is studied.In the third chapter, by using monotone iterative technique, the existence anduniqueness of common fixed point theorems of three self-mappings are studied in thecone metric space.In the forth chapter, the existence of common fixed point for expanding mappingpairs is discussed in complete cone metric space. And the fixed point theorems for thegeneralized expanding mapping pairs are also given.