In this paper, the problem of energy efficiency in cellular heterogeneous networks (HetNets) is investigated using radio resource and power management combined with the base station (BS) ON/OFF switching. The objective is to minimize the total power consumption of the network while satisfying the quality of service (QoS) requirements of each connected user. We consider the case of co-existing macrocell BS, small cell BSs, and private femtocell access points (FAPs). Three different network scenarios are investigated, depending on the status of the FAPs, i.e., HetNets without FAPs, HetNets with closed FAPs, and HetNets with semi-closed FAPs. A unified framework is proposed to simultaneously allocate spectrum resources to users in an energy efficient manner and switch off redundant small cell BSs. The high complexity dual decomposition technique is employed to achieve optimal solutions for the problem. A low complexity iterative algorithm is also proposed and its performances are compared to those of the optimal technique. The particularly interesting case of semi-closed FAPs, in which the FAPs accept to serve external users, achieves the highest energy efficiency due to increased degrees of freedom. In this paper, a cooperation scheme between FAPs and mobile operator is also investigated. The incentives for FAPs, e.g., renewable energy sharing and roaming prices, enabling cooperation are discussed to be considered as a useful guideline for inter-operator agreements.