# PROXIMAL POINTS METHODS FOR GENERALIZED IMPLICIT VARIATIONAL-LIKE INCLUSIONS IN BANACH SPACES

• He, Xin-Feng ;
• Lou, Jian ;
• He, Zhen
• Received : 2011.02.16
• Accepted : 2011.09.26
• Published : 2012.01.31
• 30 5

#### 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.

#### Keywords

generalized implicit variational-like inclusions;$J^{\eta}$-Proximal operator;Algorithm;$J^{\eta}$-proximal operator equations

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