scholarly journals An Iterative Approximation Method for a Common Fixed Point of Two Pseudocontractive Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Approximation Method ◽  
Finite Family ◽  
Convex Minimization Problem ◽  
Iterative Approximation ◽  
Pseudocontractive Mappings ◽  
The Common ◽  
Iterative Approximation Method ◽  
Fixed Point Sets

We introduce an iterative process for finding an element in the common fixed point sets of two continuous pseudocontractive mappings. As a consequence, we provide an approximation method for a common fixed point of a finite family of pseudocontractive mappings. Furthermore, our convergence theorem is applied to a convex minimization problem. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings.

scholarly journals A New Composite General Iterative Scheme for Nonexpansive Semigroups in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Pongsakorn Sunthrayuth ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Duality Mapping ◽  
Strong Convergence Theorem ◽  
Iterative Approximation ◽  
Nonexpansive Semigroups ◽  
Weakly Continuous ◽  
Weakly Continuous Duality Mapping ◽  
Iterative Approximation Method

We introduce a new general composite iterative scheme for finding a common fixed point of nonexpansive semigroups in the framework of Banach spaces which admit a weakly continuous duality mapping. A strong convergence theorem of the purposed iterative approximation method is established under some certain control conditions. Our results improve and extend announced by many others.

Hybrid Iterative Approximation Method for a Fixed Point of Nonexpansive Mapping and Equilibrium Problem

2014 ◽  
Vol 568-570 ◽  
pp. 789-792
Author(s):  
Huang Xiang Zhang ◽  
Yan Hao ◽  
Ze Hong
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Scheme ◽  
Iterative Approximation ◽  
Iterative Approximation Method

In this paper, a iterative method for approximating equilibrium problem and a fixed point of nonexpansive mappings was introduced in Hilbert spaces. And a strong convergence theorems of the iteration scheme was established. The results improve and extend the corresponding results of many others.

scholarly journals Control of Nonlinear Distributed Parameter Systems Based on Global Approximation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Chunyan Du ◽  
Guansheng Xing
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode ◽  
Linear Time ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Global Approximation ◽  
Iterative Approximation ◽  
Control Techniques ◽  
Time Varying Systems ◽  
Iterative Approximation Method

We extend an iterative approximation method to nonlinear, distributed parameter systems given by partial differential and functional equations. The nonlinear system is approached by a sequence of linear time-varying systems, which globally converges in the limit to the original nonlinear systems considered. This allows many linear control techniques to be applied to nonlinear systems. Here we design a sliding mode controller for a nonlinear wave equation to demonstrate the effectiveness of this method.

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