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

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.

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.

Cite this paper

nullLiu, W. and Meng, J. (2012) Algorithm of Iterative Process for Some Mappings and Iterative Solution of Some Diffusion Equation.*Open Journal of Applied Sciences*, **2**, 62-65. doi: 10.4236/ojapps.2012.24B015.

nullLiu, W. and Meng, J. (2012) Algorithm of Iterative Process for Some Mappings and Iterative Solution of Some Diffusion Equation.

References

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[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.