This paper extends the notion of a p-hyponormal operator to bounded right linear quaternionic operators defined on right quaternionic Hilbert spaces. Several fundamental properties known for complex p-hyponormal operators are investigated in the quaternionic setting. To develop these results, we establish the Furuta inequality for quaternionic positive operators. This inequality provides the foundation for discussing the p-hyponormality of quaternionic operators and their Aluthge transforms. Finally, we introduce a new class of quaternionic operators lying between quaternionic p-hyponormal and quaternionic paranormal operators.

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