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Benaissa, Bouharket; Azzouz, Noureddine

Reverse inequalities through \(k\)-weighted fractional operators with two parameters. (English) Zbl 1541.26037

Kyungpook Math. J. 64, No. 1, 31-46 (2024).
Summary: The aim of this paper is to present an approach to improve reverse Minkowski and Hölder-type inequalities using \(k\)-weighted fractional integral operators \({}_{a^+} \mathfrak{J}_w^{\mu}\) with respect to a strictly increasing continuous function \(\mu\), by introducing two parameters of integrability, \(p\) and \(q\). For various choices of \(\mu\) we get interesting special cases.

MSC:

26D10 Inequalities involving derivatives and differential and integral operators
26A33 Fractional derivatives and integrals
26D15 Inequalities for sums, series and integrals

Keywords:

\(k\)-weighted fractional integral operator; Minkowski inequality; Hölder inequality; \(k\)-Riemann-Liouville; \(k\)-Hadamard; \(k\)-Katugompola; \(k\)-conformable
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References:

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