Algorithm of Iterative Process for Some Mappings and Iterative Solution of Some Diffusion Equation

Wenjun Liu, Jinghua Meng

Department of Mathematics Jiujiang University Jiujiang , China.

DOI: 10.4236/ojapps.2012.24B015                

Abstract

In Hilbert spaces , through improving some corresponding conditions in some literature and extending some recent relevent results, a strong convergence theorem of some implicit iteration process for pesudocon-traction mappings and explicit iteration process for nonexpansive mappings were established. And by using the result, some iterative solution for some equation of response diffusion were obtained.

Keywords

pesudocon-traction mappings; nonexpansive mappings; implit iteration process; explicit iteration process; diffusion equation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Deimling K. zeros of accretive operators [J].Manuscripta Math, 1974,13(4):365-374.
[2]	Chang S S. Cho Y J. Zhou H Y. Iterutive methods for nonlinear operator Equation in Banach space [M].New York: Science publishers, 2002.
[3]	Zhou H Y. Convergence theorems of common fixed points for a finite family of Lipschitzian pseudocontractions inBanachspaces [J].Nonlinear Anal ,2008,68(10):2977-2983
[4]	Xu H K. Inequalities in Banach space with applications, Nonlinear Anal TMA ,1991,16(2):1127-1138.
[5]	Xu H K. Iterative algorithms for nonlinear operator [J]. J London Math Soc,2002,66:240-256.
[6]	Moudafi A. Viscosity approximation methods for fixed-points problems [J]. J Math Anal Appl.2000,241:46-55.
[7]	Xu H K. Viscosity approximation methods for nonexpa nsive mapping [J]. J Math Anal Appl,2004,298:279-291.