| Summary: | In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of <i>d</i>-tuples of <i>A</i>-bounded linear operators acting on a complex Hilbert space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">H</mi></semantics></math></inline-formula>, which leads to the special case of the well-known <i>A</i>-numerical radius for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>. Here, <i>A</i> is a positive operator on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">H</mi></semantics></math></inline-formula>. Some inequalities related to the Euclidean operator <i>A</i>-seminorm of <i>d</i>-tuples of <i>A</i>-bounded operators are proved. In addition, under appropriate conditions, several reverse bounds for the <i>A</i>-numerical radius in single and multivariable settings are also stated.
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