We introduce the concepts of a strong implicative hyper BCK-ideal and a strong positive implicative hyper BCK-ideal in hyper BCK-algebras, and investigates some related properties. Also we introduce the notions of a maximal hyper BCK-ideal and boundedness in hyper BCK-algebras, and investigates some related properties. First, we show that every strong (positive) implicative hyper BCK-ideal is a strong hyper BCK-ideal and (positive) implicative hyper BCK-ideal, but the converse is not true. Also we obtain the equivalent condition of strong implicative hyper BCK-ideals and strong hyper BCK-ideals, and we discuss the relations between strong positive implicative hyper BCK-ideals and strong implicative hyper BCK-ideals. Next, we show that if H is a bounded hyper BCK-algebra and jHj 2, then H has at least one maximal strong hyper BCK-ideal, and if H is a bounded hyper BCKalgebra and I is a proper strong (positive) implicative hyper BCK-ideal of H, then there is a maximal strong (positive) implicative hyper BCK-ideal containing I.
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