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We studied the propagation of small-amplitude dust ion acoustic (DIA) solitary waves in four-component relativistic plasma comprised of nonthermal electrons, mobile positively charged ions, positron beam and negatively charged massive dust particles. By using the reductive perturbation method, the Korteweg–de-Vries (KdV) nonlinear wave equation is derived numerically. In this work, we have elucidated the role of energetic positron beam in the relativistic plasma and analyzed the existence region for ion-acoustic (IA) solitary wave formation. It is found that for certain plasma parameters, the propagation of both compressive and rarefactive solitary waves is possible. Here, the injecting streaming positron beam in plasma gives rise to the increase in the phase velocity (Mach number) and reaches up to the hypersonic regime of flow velocity. It is observed that the initial increase in relativistic factor of positron beam , as well as temperature ratio of the positron beam to electrons decrease the characteristic features (the amplitude) of the compressive solitary wave potential profiles. On the other hand, on increasing dust grain charge , positron beam concentration ratio as well as nonthermal electrons concentration result in enhancement of the amplitudes of IA solitary wave potential profiles. The findings of this work can be more helpful in understanding the Earth's upper atmosphere (Aurora region of the ionosphere) as well as the space plasmas. [ABSTRACT FROM AUTHOR]