Choquet integral analytic inequalities
DOI:
https://doi.org/10.24193/subbmath.2020.1.02Keywords:
Choquet integral, distorted Lebesgue measure, analytic inequalities, fractional inequalities, monotonicity and convexity.Abstract
Based on an amazing result of Sugeno [15], we are able to transfer classic analytic integral inequalities to Choquet integral setting. We give Choquet integral inequalities of the following types: fractional-Polya, Ostrowski, fractional Ostrowski, Hermite-Hadamard, Simpson and Iyengar. We provide several examples for the involved distorted Lebesgue measure.
Mathematics Subject Classification (2010): 26A33, 26D10, 26D15, 28A25.
References
Anastassiou, G.A., Fractional Differentiation Inequalities, Springer, Heidelberg, New York, 2009.
Anastassiou, G.A., On right fractional calculus, Chaos, Solitons and Fractals, 42(2009), 365-376.
Anastassiou, G.A., Advances on Fractional Inequalities, Springer, Heidelberg, New York, 2011.
Anastassiou, G.A., Intelligent Comparisons: Analytic Inequalities, Springer, Heidelberg, New York, 2016.
Canavati, J.A., The Riemann-Liouville integral, Nieuw Archief Voor Wiskunde, 5(1987), no. 1, 53-75.
Choquet, G., Theory of capacities, Ann. Inst. Fourier (Grenoble), 5(1953), 131-295.
Denneberg, D., Non-additive Measure and Integral, Kluwer Academic Publishers, Boston, 1994.
Diethelm, K., The Analysis of Fractional Differentiation Equations, Springer, Heidelberg, New York, 2010.
Frederico, G.S., Torres, D.F.M., Fractional optimal control in the sense of Caputo and the fractional Noether’s theorem, International Mathematical Forum, 3(2008), no. 10, 479-493.
Iyengar, K.S.K., Note on an inequality, Math. Student, 6(1938), 75-76.
Ostrowski, A., U¨ber die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert, Comment. Math. Helv., 10(1938), 226-227.
Polya, G., Ein mittelwertsatz fu¨r Funktionen mehrerer Ver¨anderlichen, Tohoku Math. J., 19(1921), 1-3.
Polya, G., Szego¨, G., Aufgaben und Lehrs¨atze aus der Analysis, (German), Vol. I, Springer-Verlag, Berlin, 1925.
Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integrals and Derivatives, Theory and Applications, (Gordon and Breach, Amsterdam, 1993) [English translation from the Russian, Integrals and Derivatives of Fractional Order and Some of Their Applications (Nauka i Tekhnika, Minsk, 1987)].
Sugeno, M., A note on derivatives of functions with respect to fuzzy measures, Fuzzy Sets Syst., 222(2013), 1-17.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
