Convergence Analysis Of Several Iterative Algorithms In Banach Spaces

In this thesis,several generalized iterative algorithms of nonlinear operators in Ba-nach spaces are studied by combining fixed point problem,variational inequality problem,inclusion problem,equilibrium problem and split common fixed point problem.We use dual mapping,semi-closed principle and inertial viscous technique to give convergence analysis of iterative algorithms for different types of nonlinear operators.In chapter 1,we introduce the background and research status of iterative approxi-mation algorithms for nonlinear operator.The main results of this thesis are given.In chapter 2,we introduce some basic concepts of iterative approximation algorithms for nonlinear operators and give some lemmas needed in this thesis.In chapter 3,we study the following inertial implicit splitting iterative algorithm in Banach spaces:(?)The strong convergence theorem of the iterative algorithm is obtained.We extend the main results to solve the convex minimization problem.Moreover,the numerical experi-ments are presented to support the feasibility and efficiency of the proposed method.In chapter 4,we consider the following generalized viscosity implicit iteration algo-rithm in Banach spaces:#12 The strong convergence theorem of this algorithm is proved,which solves the variational inequality problem.We provide some applications to zero point problems and equilibrium problems.Further,a numerical example is given to illustrate the convergence analysis.In chapter 5,we give a system of generalized variational inequalities in Banach spaces:(?)and study the following iterative algorithm of general variational inequality system:(?)which converges strongly to a common element of the fixed point set of an asymptotical-ly non-expansive mapping and the set of solutions of the general variational inequality system.A numerical experiment is given to show the implementation and efficiency of the main theorem.In chapter 6,we study the following iterative algorithm for equilibrium and fixed point problems in Banach spaces:(?)which converges strongly to a common solution of a system of equilibrium problems and a fixed point problem of a Bregman relatively non-expansive mapping.Numerical examples are given to prove the effectiveness of the algorithm.In chapter 7,we study the following iterative algorithm for splitting common fixed point problems in Banach spaces:(?)which converges strongly to a solution of split common fixed point problem for Bregman quasi-non-expansive mappings.As an application,the results are applied to solving zero problem and equilibrium problem.In chapter 8,we make a conclusion and give some problems for further exploration.