  Splitting algorithms for finding a zero of sum of operators often involve
multiple steps which are referred to as forward or backward steps. Forward
steps are the explicit use of the operators and backward steps involve the
operators implicitly via their resolvents. In this paper, we study an adaptive
splitting algorithm for finding a zero of the sum of three operators. We assume
that two of the operators are generalized monotone and their resolvents are
computable, while the other operator is cocoercive but its resolvent is missing
or costly to compute. Our splitting algorithm adapts new parameters to the
generalized monotonicity of the operators and, at the same time, combines
appropriate forward and backward steps to guarantee convergence to a solution
of the problem.
