Maximal Monotonicity of the Operator S+A^*TA under w^*-Closed Condition

In this paper, we introduce a sufficient condition for maximality of the operator $S+A^*TA$, where $S:X\multimap X^*$ and $T:Y\multimap Y^*$ are two maximal monotone operators, $A:X\rightarrow Y$ is a continuous linear mapping with the adjoint $A^*$ and $X$, $Y$ are reflexive Banach spaces. By using representative function of $S$ and $T$ we introduce a representative function for $S+A^*TA$ that proves $S+A^*TA$ is a maximal monotone operator.