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<p/> <p>A new monotonicity, <inline-formula><graphic file="1687-1812-2007-076040-i1.gif"/></inline-formula>-monotonicity, is introduced, and the resolvant operator of an <inline-formula><graphic file="1687-1812-2007-076040-i2.gif"/></inline-formula>-monotone operator is proved to be single-valued and Lipschitz continuous. With the help of the resolvant operator, the positively semidefinite general variational inequality (VI) problem VI <inline-formula><graphic file="1687-1812-2007-076040-i3.gif"/></inline-formula> is transformed into a fixed point problem of a nonexpansive mapping. And a proximal point algorithm is constructed to solve the fixed point problem, which is proved to have a global convergence under the condition that <inline-formula><graphic file="1687-1812-2007-076040-i4.gif"/></inline-formula> in the VI problem is strongly monotone and Lipschitz continuous. Furthermore, a convergent path Newton method is given for calculating <inline-formula><graphic file="1687-1812-2007-076040-i5.gif"/></inline-formula>-solutions to the sequence of fixed point problems, enabling the proximal point algorithm to be implementable.</p>