Patra, A.Roy, F.2026-02-042024Operators and Matrices, 2024, 18, 2, pp. 343-35918463886https://doi.org/10.7153/oam-2024-18-21https://idr.nitk.ac.in/handle/123456789/21066The objective of this article is to estimate the q-numerical radius of bounded linear operators on complex Hilbert spaces. One of our main results states that for a bounded linear operator T in a Hilbert space H and q ∈ [0,1], the relation (Formula Presented) holds where w(T), w<inf>q</inf> (T) are the numerical radius and q-numerical radius of T respectively. Several refined new upper bounds follow from this result. Finally, the q-numerical radius of 2 × 2 operator matrices is explored and several new results are established. © 2024, Element D.O.O.. All rights reserved.operator matrixq-numerical radiusq-numerical range