Abstract
In this paper we present general quantitative estimates in terms of the modulus of continuity and of a K-functional, in approximation by the generalized multivariate Stancu-Durrmeyer-Choquet-Šipoš operators
(Communicated by Anatolij Dvurečenskij)
References
[1] Choquet, G.: Theory of capacities, Ann. Inst. Fourier (Grenoble) 5 (1954), 131–295.10.5802/aif.53Search in Google Scholar
[2] Denneberg, D.: Non-Additive Measure and Integral, Kluwer Acad. Publ., Dordrecht, 1994.10.1007/978-94-017-2434-0Search in Google Scholar
[3] Dubois, D.—Prade, H.: Possibility Theory, Plenum Press, New York, 1988.10.1007/978-1-4684-5287-7Search in Google Scholar
[4] Gal, S. G.: Approximation by Choquet integral operators, Ann. Mat. Pura Appl. 195 (2016), 881–896.10.1007/s10231-015-0495-xSearch in Google Scholar
[5] Gal, S. G.—Opris, B. D.: Uniform and pointwise convergence of Bernstein-Durrmeyer operators with respect to monotone and submodular set functions, J. Math. Anal. Appl. 424 (2015), 1374–1379.10.1016/j.jmaa.2014.12.012Search in Google Scholar
[6] Gal, S. G.—Trifa, S.: Quantitative estimates in uniform and pointwise approximation by Bernstein-Durrmeyer-Choquet operators, Carpathian J. Math. 33 (2017), 49–58.10.37193/CJM.2017.01.06Search in Google Scholar
[7] Gonska, H.—Kacsó D.—Rasa, I.: The genuine Bernstein-Durrmeyer operators revisited, Results Math. 62 (2012), 295–310.10.1007/s00025-012-0287-1Search in Google Scholar
[8] Stancu, D. D.: On a generalization of the Bernstein polynomials (Romanian), Studia Univ. Babes-Bolyai Ser. Math.-Phys. 14 (1969), 31–45.Search in Google Scholar
[9] Šipoš, J.: Integral with respect to a pre-measure, Math. Slovaca 29 (1979), 141–155.Search in Google Scholar
[10] Šipoš, J.: Nonlinear integrals, Math. Slovaca 29 (1979), 257–270.Search in Google Scholar
[11] Wang, Z.—Klir, G. J.: Generalized Measure Theory, Springer, New York, 2009.10.1007/978-0-387-76852-6Search in Google Scholar
© 2019 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular papers
- The life jubilee of Prof. RNDr. Sylvia Pulmannová, DrSc.
- Perfect 1-factorizations
- A topological duality for strong Boolean posets
- On the Diophantine equations x2 + 2α 3β 19γ = yn and x2 + 2α 3β 13γ = yn
- Tribonacci numbers and primes of the form p = x2 + 11y2
- Basic semirings
- A conjecture for varieties of completely regular semigroups
- Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets
- Differential subordination results for Mittag-Leffler type functions with bounded turning property
- Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays
- Asymptotically periodic behavior of solutions of fractional evolution equations of order 1 < α < 2
- On the polynomial entropy for morse gradient systems
- Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators
- A note on non-linear ∗-Jordan derivations on ∗-algebras
- Disjoint hypercyclic weighted translations on locally compact hausdorff spaces
- Some new results on real hypersurfaces with generalized Tanaka-Webster connection
- Relative topological properties of hyperspaces
- Cohomology of torus manifold bundles
- The Menger and projective Menger properties of function spaces with the set-open topology
- Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications
Articles in the same Issue
- Regular papers
- The life jubilee of Prof. RNDr. Sylvia Pulmannová, DrSc.
- Perfect 1-factorizations
- A topological duality for strong Boolean posets
- On the Diophantine equations x2 + 2α 3β 19γ = yn and x2 + 2α 3β 13γ = yn
- Tribonacci numbers and primes of the form p = x2 + 11y2
- Basic semirings
- A conjecture for varieties of completely regular semigroups
- Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets
- Differential subordination results for Mittag-Leffler type functions with bounded turning property
- Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays
- Asymptotically periodic behavior of solutions of fractional evolution equations of order 1 < α < 2
- On the polynomial entropy for morse gradient systems
- Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators
- A note on non-linear ∗-Jordan derivations on ∗-algebras
- Disjoint hypercyclic weighted translations on locally compact hausdorff spaces
- Some new results on real hypersurfaces with generalized Tanaka-Webster connection
- Relative topological properties of hyperspaces
- Cohomology of torus manifold bundles
- The Menger and projective Menger properties of function spaces with the set-open topology
- Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications