Distribution locational marginal pricing (DLMP) can adversely affect users in a grid-constrained transactive distribution system market (DSM) that are at a distance away from the substation, requiring longer paths to connect to the substation. When the grid operates closer to its physical limits in terms of line capacities and voltage deviations, these users are more likely to cause grid violations than others in the vicinity of the substation. Conversely, increased energy consumption by users near the substation can choke off the supply to those at the grid s extremities. This research describes a novel mechanism to charge users in a more equitable manner, by regularizing the distribution system operator (DSO)s social welfare based objective function with a fairness criterion. The Jains index of fairness is used in this context and corresponding fairness DLMP component is derived. The overall problem entails the maximization of the regularized objective within a set of linear constraints. The constraints that ensure that the grids voltage and line power limits are not violated. Constrained optimization is carried out in an iterative manner through dual decomposition where the dual variables and unit costs are incrementally updated by the DSO using the augmented Lagrangian method (ALM). Simulations reported in this study confirm the effectiveness of the proposed approach.