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The present paper introduces a kind of Kantorovich type Shepard operators. Complete results including direct and converse results, equivalence results are established. As Della Vecchia and Mastroianni ([4], [7]) did, our results involve a weighted modulus of smoothness related to step‐functions  φ  ( x ) vanishing algebraically at the endpoints ±1 (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)