In this study, considering slippage between a robot end-effector and an object, adaptive control of a one-finger hand manipulating an object is explored. This system is a good sample to develop different techniques such as grasp analysis, grasp synthesis, stability analysis and designing different types of controller for cooperative manipulator systems. Due to the presence of inequality equations in frictional point contact modeling, a novel formulation is developed to replace the equality and inequality equations with a single second order differential equation with switching coefficients. Introducing this new friction contact model, an input-output conventional form is derived using the equality and inequality equations of motion of the system. Using this new form of motion equations, two adaptive controllers with simple update laws are proposed that both of them ensure the asymptotic convergence of the object position tracking as well as slippage control while compensating the system uncertainties. The first controller compensates the uncertain masses of the manipulator links and the object while the second one compensates the uncertain coefficients of friction. Numerical simulation is utilized to evaluate performance of the proposed controllers.