Research On Fixed Point And Variational Inclusion

In the Hilbert space,this essay presents an iterative algorithm to approximate the fixed point of Lipschitz pseudocontractive mapping.The construction of this iterative algorithm overcomes the problem that the Mann algorithm does not necessarily converge to the fixed point of Lipschitz pseudocontractive mapping,and the strong convergence analysis of the algorithm is given under appropriate assumptions.In addition,an iterative algorithm is proposed to find a common solution of the quasi-variational inclusion and fixed point problem,and the strong convergence analysis of the algorithm is given under appropriate assumptions.In the Hilbert space,an iterative algorithm is proposed to solve the common solution problem of fixed point and split variational inclusions,and the strong convergence analysis of the algorithm is given under appropriate assumptions.This essay consists of five parts:the first part introduces the development process of pseudocontractive class and variational inequality,and give the research status and significance of several kinds of pseudocontractive,variational inclusion and variational inequality.In the second part,based on the existing Mann algorithm,the iterative algorithm in this essay is proposed to approximate the fixed point of pseudocontractive mapping,the strong convergence analysis of the proposed algorithm is given under appropriate assumptions.In the third part,based on the existing Hartman-Stampacchia variational inequality,an iterative algorithm is proposed to solve the approximation problem of fixed point and quasi-variational inclusion,and the strong convergence analysis of the algorithm is given under appropriate assumptions.In the fourth part,we introduce an interative algorithm for finding a common solution of the split variational inclusion problem and fixed point problem of a quasi-pseudocontractive operator and the strong convergence theory of the algorithm is obtained under appropriate assumptions.The fifth part is a review of this essay and a prospect of future research in related fields,hoping that this kind of problems can be more promoted and applied.