OICC Press Mathematical Analysis and its Contemporary Applications 7 4 2025 11 10 On Fuglede-Putnam property and orthogonality for derivations induced by hyponormal operators 10.30495/maca.2025.2073114.1150 EN David Kagali Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo, Kenya Benard Okelo Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo, Kenya https://orcid.org/0000-0003-3963-1910 Julia Owino Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo, Kenya Journal Article 2025 11 10 The orthogonality of derivations induced by operators is an area with various applications in light of ever-dynamic technological advances. There are different types of orthogonality, and interesting results have emerged in which operators satisfying given conditions are chosen to establish Range-Kernel orthogonality. However, most of the results have focused on one type of orthogonality called the Birkhoff orthogonality. We have also herein considered the Birkhoff concept of orthogonality. Researchers have repeatedly posed the following question: Could there be a possibility for studying other types of orthogonality with respect to the range and the kernel of derivations apart from the Birkhoff orthogonality? In this note, we establish orthogonality conditions for derivations when implemented by hyponormal operators under the Fuglede-Putnam property.