Minimum-norm Fixed Point Of Nonexpansive Mappings

The fixed point of nonexpansive mappings is widely used in modern mathematics, such as in nonlinear hemigroups, ergodic theorem and the theorem of monotone operator. Mminimum-norm fixed point is a kind of fixed point that satisfies the property of lest-norm, which is used broadly as well as fixed point. For instance, in the least-squares problems, the least-norm solutions are used to define the pseudoinverse of bounded linear operators, further more, it is aslo used in finding the solutions of minimization problem. So it is improtant for us to do the reserch in this field. The main contents of this paper are as follows:1.After the introduction of Nonlinear Function Analysis, the realm of fixed point and the research approach of this paper are presented, respectively.2.In Hilbert space, the famous methods of Browder's and Halpern's are used in finding the minimum-norm fixed point of nonexpansive self-mapping,meanwhile, an application in minimization problem is also included, at the same time, the above two methods are expanded.3.In Hilbert space, under the discussion of 1, another question arising about finding the minimum-norm fixed point of a nonexpansive non-self mapping which satisfies the weak inwardness condition.4.In Hilbert space, a new kind of nonexpansive mappings (that is a finite family of nonexpansive mappings) is introduced and studied, both cyclic and parallel iteration methods are introduced to find the common minimal-norm fixed points of a finite family of nonexpansive mappings.