Motivated by previously reported results by our partner researcher, this work aims to provide new refinements of both vector and numerical radius inequalities by presenting an improved version of the well-known Buzano inequality, which consequently yields an additional refinement of the Cauchy–Schwarz (CS) inequality. By utilizing these new refinements of the Buzano and Cauchy–Schwarz inequalities, we proceed to establish several related vector and numerical radius-type inequalities.
The methods employed in this paper are standard within the field of operator theory inequalities.
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