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Viscosity methods of approximation for a common solution of a finite family of accretive operators

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In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

Abstract

In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

참고문헌 (13)

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  3. Chen Junmin, "Viscosity Approximation Methods for Nonexpansive Mappings and Monotone Mappings", J. Math. Anal. Appl, 334, pp.1450~1461 (2007)
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  6. Jong Soo Jung, "Strong convergence of an iterative method for finding common zeros of a finite family of accretive operators", 대한수학회논문집, 24(3), pp.381~393 (2009), 대한수학회
  7. Moudafi A., "Viscosity Approximation Methods for Fixed-Points Problems", J. Math. Anal. Appl, 241, pp.46~55 (2000)
  8. Paul-Emile Mainge, "Viscosity methods for zeros of accretive operators", J. Approximation Theory, 140, pp.127~140 (2006)
  9. Suziki T., "Strong convergence theorems for in nite families of nonexpansive mappings in general Banach spaces", Fixed Point Theory Appl, 1, pp.103~123 (2005)
  10. Takahashi W., "Nonlinear Function Analysis-Fixed Point Theory and its Applications" (2000), Yokohama Publishers
  11. Xu H. K., "An iterative approach to quadratic optimization", J. Optim. Theory Appl, 116, pp.659~678 (2003)
  12. Xu H. K., "Viscosity approximation methods for nonexpansive mappings", J. Math. Anal. Appl, 298, pp.279~291 (2004)
  13. Zegeye H., "Strong convergence theorems for a common zero of a family of m-accretive mappings", Nonlinear Anal, 66, pp.1161~1169 (2007)

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