Planar and nonplanar dust acoustic (DA) solitary waves are studied in an unmagnetized plasma consisting of electrons, positrons, ions and dust species. This is done by deriving the modified Kortweg–de Vries (mKdV) equation under the small amplitude perturbation expansion method. It is found that in the presence of positrons, DA hump-like solitary waves may also exist under suitable conditions. It is also observed that the positron concentration and the ratio of ion-to-electron temperature significantly modify the propagation characteristics of DA solitary waves. The range of plasma parameters for which we obtain hump-like solitons are found numerically. The present investigation may have relevance in both laboratory and astrophysical plasmas.