Abstract This paper focuses on establishing new generalizations of Hilbert-type inequalities on arbitrary time scales. We present three main theorems on weighted integral inequalities involving a nonnegative homogeneous kernel. The proofs rely on several auxiliary lemmas together with the effective application of Hölder’s inequality. By specializing our results to the continuous time scale (T=R T = R) and the discrete time scale (T=N T = N), we derive a number of corollaries that unify and extend both classical and recent inequalities. Overall, this work contributes to the theory of integral inequalities by providing a broader framework and new analytical tools within the calculus on time scales.
Mohamed et al. (Mon,) studied this question.
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