Kantorovich-type Integral Inequalities and Their Fractional Extensions
DOI:
https://doi.org/10.63286/jima.029Keywords:
Kantorovich inequality, weighted inequalities, Riemann-Liouville fractional integralAbstract
We establish sharp Kantorovich-type inequalities for Lebesgue integrable functions bounded between two positive constants. By constructing extremal piecewise constant functions and applying classical techniques, we derive precise upper bounds for the ratio of L2 and L1 norms and extend the results to weighted settings. Furthermore, we generalize the inequalities to the framework of the Riemann–Liouville fractional integral of order α∈(0,1], capturing nonlocal behaviour and memory effects. These results refine known inequalities and provide sharper analytical tools for applications in classical and fractional analysis.
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Copyright (c) 2025 Mehmet Zeki Sarıkaya
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