Dissertation > Excellent graduate degree dissertation topics show

Several Fixed Point Theorems、 Iterative Schemes and Their Appliction

Author: ZhangYan
Tutor: ZhangCongJun
School: Nanjing University of Finance and Economics
Course: Applied Mathematics
Keywords: fixed point theorem iterative algorithm asymptotically k-strict pseudo-contraction
CLC: O177.91
Type: Master's thesis
Year: 2011
Downloads: 61
Quote: 0
Read: Download Dissertation

Abstract


The fixed point theory takes a great important space on math and its applications. The development of fixed point problem brought great convenience to solve the problems of the equation and physics. Fixed point problems have close relationship with optimization problems, maximum and minimum problems, complementarity problems, variational inequality problems and equilibrium problems.In this paper,we studied the existence of the fixed point on some mappings, such as contraction mappings and expansive mappings in some spaces, got the iterative algorithm of the fixed point and studied the applications to differential equations and the equilibrium problems. This paper is divided into three parts:In the first chapter, we showed the introductions and some preliminaries. In the second chapter, in metric space, we discussed the existence of fixed points with promoted expansive mapping and the contraction mapping application to differential equations with two ordinary point; in topological linear space, we used the fixed point existence theorem to solve the equilibrium problem with upper and lower bounded and the equilibrium problems with lower and upper bounds and restricted conditions; in cone metric spaces, we studied the existence of fixed points with a general contraction mapping; in fuzzy metric spaces, discussed the existence of the fixed points theorem and the fixed point can be found by PK algorithm. In the third chapter, at first, we studied the fixed point of asymptotically k-strict pseudo-contraction mapping, proved weak and strong convergence of its iterative sequence, then showed weak and strong convergence theorems of the intersection between the solution of the equilibrium problem and fixed point problem under modified Ishikawa algorithms.In some way, the conclusions above have not only improved the conclusions some scholars have already got, but also we showed some examples and applications about relative conclusions.

Related Dissertations

  1. Positive Solutions of Boundary Value Problems for Nonlinear Ordinary Differential Equations,O175.8
  2. The Exitence and Algorithm of Solution for Variational Inequality and Variational Inclusion,O178
  3. Design and Implementation on Signal Processing Algorithm for Power Quality Monitoring System,TN911.7
  4. Wavelets-based Signal Sparse Representation and Its Application in Image Denoising,TP391.41
  5. Study on a Class of Sturm-Liouville Boudary Value Problems,O175.8
  6. Two kinds of fractional differential equations with nature,O175
  7. Local Null Controllability of Semilinear Parabolic Equation,O175.26
  8. Positive Solutions for Second Order Differentiae Equations Boundary Value Problem on the Half-line,O175.8
  9. Non- local Higher Order Differential Equations Boundary Value Existence,O175.8
  10. About ODE (k, nk) conjugate boundary value problems,O175.8
  11. The Existence of Positive Solutions for Boundary Value Problems for Two Calss of Differential Equation Systems with the Frist Order Derivative,O175.8
  12. Radial Shearing Interferometry Test Technology,TH744.3
  13. Based on the fixed point theory of second-order differential equations Stability,O175.13
  14. The Property of the Solution for Vetor Equilibrium Problems in Lexicographic Order,O177
  15. On Existences of Solutions for Generalized Variational Inequality Problems,O178
  16. The Researching and the Simulation of Solar Array Simulator,TM914.4
  17. The Study of Projection Sorting and Subset Selection in Iterative Reconstruction Algorithm Based on Cone-beam CT,TP391.41
  18. Existence of Solutions of Boudary Value Problem for Nonlinear Fractional Functional Differential Equations,O175.8
  19. Bring Lower Bounds for Equilibrium Problems Existence of Solutions Xing , stability analysis and Its Algorithm,O177
  20. Iterative Methods for Extended General Mixed Variational Inequalities,O178
  21. Research on the Integrated Production-inventory Optimal Model in CPFR,F253.4

CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Nonlinear Functional Analysis
© 2012 www.DissertationTopic.Net  Mobile