Abstract
Here we study the quantitative mixed conformable and iterated fractional approximation of positive sublinear operators to the unit operator. These are given a precise Choquet integral interpretation. Initially we start with the research of the mixed conformable and iterated fractional rate of the convergence of the well-known Bernstein-Kantorovich–Choquet and Bernstein–Durrweyer–Choquet polynomial Choquet-integral operators.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
T. Abdeljawad, On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)
G. Anastassiou, Iterated fractional approximation by Max-Product operators (2017). submitted
G. Anastassiou, Mixed Conformable and Iterated fractional Approximation by Choquet integrals, Progress in Fractional Differentiation and Applications (2018). Accepted
G. Anastassiou, Advanced fractional Taylor’s formulae. J. Comput. Anal. Appl. 21(7), 1185–1204 (2016)
G. Anastassiou, Mixed conformable fractional approximation by sublinear operators. Indian J. Math. 60(1), 107–140 (2018)
G. Anastassiou, I. Argyros, Intelligent Numerical Methods: Applications to Fractional Calculus (Springer, New York, 2016)
G. Choquet, Theory of capacities. Ann. Inst. Fourier (Grenoble) 5, 131–295 (1954)
D. Denneberg, Non-additive Measure and Integral (Kluwer, Dordrecht, 1994)
D. Dubois, H. Prade, Possibility Theory (Plenum Press, New York, 1988)
S. Gal, Uniform and Pointwise quantitative approximation by Kantorovich-Choquet type integral Operators with respect to monotone and submodular set functions. Mediterr. J. Math. 14(5), 12 (2017). Art. 205
S. Gal, S. Trifa, Quantitative estimates in uniform and pointwise approximation by Bernstein-Durrmeyer-Choquet operators. Carpathian J. Math. 33(1), 49–58 (2017)
R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)
Z.M. Odibat, N.J. Shawagleh, Generalized Taylor’s formula. Appl. Math. Comput. 186, 286–293 (2007)
D. Schmeidler, Integral representation without additivity. Proc. Am. Math. Soc. 97, 255–261 (1986)
D. Schmeidler, Subjective probability and expected utility without additivity. Econometrica 57, 571–587 (1989)
L.S. Shapley, A value for n-person games, in Contributions to the Theory of Games, Annals of mathematical studies 28, ed. by H.W. Kuhn, A.W. Tucker (Princeton University Press, 1953), pp. 307–317
Z. Wang, G.J. Klir, Generalized Measure Theory (Springer, New York, 2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Anastassiou, G.A. (2019). Mixed Conformable and Iterated Fractional Quantitative Approximation by Choquet Integrals. In: Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators. Studies in Systems, Decision and Control, vol 190. Springer, Cham. https://doi.org/10.1007/978-3-030-04287-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-04287-5_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-04286-8
Online ISBN: 978-3-030-04287-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)