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Some improvements of Hölder’s inequality on time scales. (English) Zbl 1424.26075
Summary: The theory and applications of dynamic derivatives on time scales have recently received considerable interest. In this paper, we define a function using the combined diamond-\(\alpha\) integral, investigate its monotonicity and give some refinements for Hölder’s inequality. We present some applications for \(\mathbb Z\) and \(\mathbb R\).
MSC:
26E70 Real analysis on time scales or measure chains
26D15 Inequalities for sums, series and integrals
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