Spectral efficiency in cognitive radio network (CRN) can be achieved by allowing unlicensed users or secondary users (SUs) to coexist with legacy spectrum holders or primary users (PUs) in the same spectrum band, either on an opportunistic or cooperative basis. Relay based cooperative spectrum sharing (CSS) is a promising technique for maximizing spectrum utilization as well as Utility of the users in overlay CRNs. This paper proposes a relay based CSS scheme to increase the cooperative capacity of PU network in a single-PU multi-SU overlay CRN scenario. Based on the characteristics and Quality of Service (QoS) requirements of PU services, the CSS is modelled either as bandwidth sharing or as time sharing problem. Our objective is to assign most profitable SU as a relay to the PU and allocate optimal resource (bandwidth or time) between them, such that PU can maximize its Utility with minimum possible cost incurred and satisfies the compensation constraint of cooperative relay node. Concerning the non-linearity and computationally hard nature of the proposed optimization problem, a quick iterative heuristic solution based on numerical analysis method is proposed and obtain near-optimal solution in polynomial time. Simulation based experimental results show that the proposed approaches succeed in meeting the service requirements of the PU with maximum Utility achievement than the conventional approaches. The proofs of non-linearity and convergence of the proposed algorithm are demonstrated in the paper.