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In this paper, we study first the concept of p-sequentially Right property, which is p-version of the sequentially Right property. Also, we introduce a new class of subsets of Banach spaces which is called p-Right * set and obtain the relationship between p-Right subsets and p-Right * subsets of dual spaces. Furthermore, for 1 ≤ p < q ≤ ∞, we introduce the concepts of properties (SR) p,q and (SR * ) p,q in order to find a condition such that every Dunford-Pettis q-convergent operator isdoi:10.2298/fil1914461a fatcat:pj7ty5lvyrdqxe7us3kw2zf7qy