East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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PROXIMAL POINTS METHODS FOR GENERALIZED IMPLICIT VARIATIONAL-LIKE INCLUSIONS IN BANACH SPACES

  • He, Xin-Feng (College of Mathematics and Computer, Hebei University) ;
  • Lou, Jian (Computers Center, Hebei University) ;
  • He, Zhen (College of Mathematics and Computer, Hebei University)
  • Received : 2011.02.16
  • Accepted : 2011.09.26
  • Published : 2012.01.31
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Abstract

In this paper, we study generalized implicit variational-like inclusions and $J^{\eta}$-proximal operator equations in Banach spaces. It is established that generalized implicit variational-like inclusions in real Banach spaces are equivalent to fixed point problems. We also establish relationship between generalized implicit variational-like inclusions and $J^{\eta}$-proximal operator equations. This equivalence is used to suggest a iterative algorithm for solving $J^{\eta}$-proximal operator equations.

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References

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