Prof. Dr. Ulrich Abel

 2010-2018

84

U. Abel, Ovidiu Furdui, Ioan Gavrea und M. Ivan, A note on a conjecture in risk theory, Czech. Math. J. 60 (2010), 1049-1053.

85

U. Abel und M. Ivan, Simultaneous approximation by Altomare operators,  Proceedings of the 6th international conference on functional analysis and approximation theory, Acquafredda di Maratea (Potenza), Italy, Sept. 24-30, 2009, Palermo: Circolo Matemàtico di Palermo, Rend. Circ. Mat. Palermo, Serie II, Suppl. 82 (2010), 177-193.

86

U. Abel, A complete asymptotic expansion for a sequence of certain sums, Appl. Math. Comput. 217 (2010), 4302-4305.

87

U. Abel und M. Ivan, A best asymptotic constant related to the operators of Bleimann, Butzer and Hahn, Result. Math. 58 (2010), 207-219.

88

U. Abel, Asymptotic expansions for Favard operators and their left quasi-interpolants, Stud. Univ. Babeş-Bolyai Math. 56 (2011), 199-206.

89

U. Abel und M. Ivan, New representation of the remainder in the Bernstein approximation, J. Math. Anal. Appl. 381 (2011), 952-956.

90

U. Abel und M. Ivan, The Bleimann-Butzer-Hahn operators: old and new results,  Appl. Anal. 90 (2011), 483-491.

91

U. Abel, P. L. Butzer und F. Schurer, On life and work of P.C. Sikkema (1919-1998), (Dutch), Nieuw Arch. Wiskd. (5) 12, No. 1, 66-72 (2011).

92

U. Abel und P. L. Butzer, Complete Asymptotic Expansion for Generalized Favard Operators,  Constr. Approx. 35, No. 1, 73-88 (2012).

Online First™, 9 June 2011, DOI: 10.1007/s00365-011-9134-y.

93

U. Abel und P. L. Butzer, Old and New Results on the Favard Operator,  CONSTRUCTIVE THEORY OF FUNCTIONS, Sozopol 2010: In memory of Borislav Bojanov (G. Nikolov and R. Uluchev, Eds.), pp. 1-8, Prof. Marin Drinov Academic Publishing House, Sofia, 2012.

94

U. Abel, Voronovskaja-type Formula for the Bézier Variant of the Bernstein Operators,  CONSTRUCTIVE THEORY OF FUNCTIONS, Sozopol 2010: In memory of Borislav Bojanov (G. Nikolov and R. Uluchev, Eds.), pp. 401-402, Prof. Marin Drinov Academic Publishing House, Sofia, 2012.

95

U. Abel, Vectorial proof of an inequality for quadrilaterals (Vektorieller

Beweis einer Ungleichung für Vierecke, Die Wurzel 46 (2012), 223.

96

U. Abel und M. Ivan, Complete asymptotic expansions for Altomare operators, Mediterr. J. Math. 10 (2013), 17-29.

97

U. Abel, M. Ivan und R. Păltănea, Geometric series of Bernstein operators revisited, J. Math. Anal. Appl. 400 (2013), 22-24.

98

U. Abel, W. Awan und V. Kushnirevych, A generalization of the gcd-sum function, J. Integer Seq. 16 (2013), No. 6, Article 13.6.7, 12 p.

99

Ulrich Abel, Wolfgang Gawronski und Thorsten Neuschel, Binomial Polynomials, Comput. Methods Funct. Theory 13:1 (2013), 163-180.

DOI 10.1007/s40315-013-0013-3

100

U. Abel, A generalization of the Leibniz Rule, Amer. Math. Monthly 120:10 (2013), 924-928.

DOI 10.4169/amer.math.monthly.120.10.924

101

U. Abel, Applications of a generalized Leibniz Rule, CONSTRUCTIVE THEORY OF FUNCTIONS, Sozopol 2013: Dedicated to Blagovest Sendov and Vasil Popov (K. Ivanov, G. Nikolov and R. Uluchev, Eds.), pp. 1-9, Prof. Marin Drinov Academic Publishing House, Sofia, 2014.

102

U. Abel, M. Ivan und R. Păltănea, Geometric series of positive linear operators and the inverse Voronovskaya theorem on a compact interval, J. Approx. Theory 184 (2014), 163-175.

DOI 10.1016/j.jat.2014.05.011

103

U. Abel, Eine Bemerkung zum Artikel „Die Waagenformel für Mittelpunkte", Die Wurzel 1/2014 (2014), 8-9.

104

U. Abel, Integration von sinc-Produkten mit funktionentheoretischen Methoden, Mathematische Semesterberichte 61 (2014), 153-158.

DOI 10.1007/s00591-013-0122-0

105

U. Abel, Slicing cakes into equal pieces (Letter to the Editor), Math. Spectrum 47:2 (2014/15), 84-86.

106

Ulrich Abel, Wolfgang Gawronski und Thorsten Neuschel, Complete monotonicity and zeros of sums of squared Baskakov functions, Appl. Math. Comput. 258 (2015), 130-137.
DOI 10.1016/j.amc.2015.01.062

107

U. Abel, A new Faà di Bruno type formula, Elem. Math. 70 (2015), 49-54.
DOI 10.4171/EM/274

108

U. Abel, M. Ivan und R. Păltănea, The Durrmeyer variant of an operator defined by D.D. Stancu, Appl. Math. Comput. 259 (2015), 116-123.
http://dx.doi.org/10.1016/j.amc.2015.02.026

109

U. Abel, On an identity involving powers of binomial coefficients, Coll. Math. J. 46 (2015), 138.
http://dx.doi.org/10.4169/college.math.j.46.2.138

110

U. Abel, V. Gupta und M. Ivan, A generalization of a combinatorial identity by Chang and Xu, Bull. Math. Sci. 5 (2015), 511-516.
DOI 10.1007/s13373-015-0072-z

111

U. Abel, Asymptotic expansion of an integral considered in a problem of IMC 2015, Gazeta Matematică, Seria A, 33 (CXII) (2015), 37-39.

112

U. Abel, Certain multiple factorial series and their asymptotic properties, Applied Mathematics E-Notes 16 (2016), 161-169.

113

U. Abel und O. Agratini, Asymptotic behaviour of Jain operators, Numer. Algorithms 71 (2016), 553-565.

DOI 10.1007/s11075-015-0009-3

114

U. Abel und O. Agratini, On the variation detracting property of operators of Balazs and Szabados, Acta Math. Hungar. 150 (2016), 383-395.

doi:10.1007/s10474-016-0642-x

115

U. Abel, High order algorithms for calculating roots, The Math. Gaz. 11 (2016), 420-428.

DOI:10.1017/mag.2016.106

116

U. Abel, A brief history of the Favard operator and its variants, Rassias, Themistocles M. (ed.) et al., Mathematical analysis, approximation theory and their applications, Cham: Springer (ISBN 978-3-319-31279-8/hbk; 978-3-319-31281-1/ebook). Springer Optimization and Its Applications 111, 1-13 (2016).

117

U. Abel, A generalization of Halphén.s formula for derivatives, Aequat. Math. 91 (2017), 115-120.

DOI 10.1007/s00010-016-0448-5

118

U. Abel, An inequality involving Bernstein polynomials and convex functions, J. Approx. Theory 222 (2017), 1-7.

http://dx.doi.org/10.1016/j.jat.2017.05.006

119

U. Abel, An identity for formal derivatives in a commutative algebra, Annales Polonici Mathematici 119 (2017), 195-202.

DOI: 10.4064/ap170324-11-9 Published online: 18 October 2017

120

U. Abel, L. Beukemann and V. Kushnirevych, Rolling Curves: An Old Proof of the Roulette Lemma, Amer. Math. Monthly 124 (2017), 723-736.

DOI: 10.4169/amer.math.monthly.124.8.723

121

U. Abel und V. Kushnirevych, Ist das logarithmische Mittel abstandserzeugt?, Die Wurzel 12/2017 (2017), 262-265.

122

U. Abel and H. Karsli, Complete Asymptotic Expansions for Bernstein-Chlodovsky Polynomials. In: CONSTRUCTIVE THEORY OF FUNCTIONS, Sozopol 2016 (K. Ivanov, G. Nikolov and R. Uluchev, Eds.), pp. 1-12, Prof. Marin Drinov Academic Publishing House, Sofia, 2017.

123

U. Abel und I. Raşa, A sharpening of a problem on Bernstein polynomials and convex functions, Math. Inequal. Appl. 21 (2018), 773-777.

doi:10.7153/mia-2018-21-55

124

U. Abel und H. Siebert, An improvement of the constant in Videnskiĭ’s inequality for Bernstein polynomials, Georgian Math. J., Online First.

https://doi.org/10.1515/gmj-2017-0065

125

U. Abel, Evaluation of a logarithmic integral, Int. J. Open Problems Compt. Math. 11 (2018), No. 1, 76-79.

126

U. Abel, The number of gridpoints on hyperplane sections of the d-dimensional cube, Proc. Amer. Math. Soc. 146 (2018), 5349-5355.

doi.org/10.1090/proc/14233

127

U. Abel, O. Agratini and R. Paltanea, A complete asymptotic expansion for the quasi-interpolants of Gauß-Weierstraß operators, Mediterr. J. Math. 15 (2018), Online First.

https://doi.org/10.1007/s00009-018-1195-8

128

U. Abel and H. Karsli, Asymptotic expansions for Bernstein-Durrmeyer-Chlodovsky polynomials, Result. Math. 73 (2018), Online First.

https://doi.org/10.1007/s00025-018-0863-0

129

U. Abel and V. Kushnirevych, On Bennett’s conjecture and complete monotonicity, Math. Inequal. Appl. 22 (2019), 165-173.

130

U. Abel, Some new identities for derangement numbers, Fibonacci Q. 56 (2018), 313-318.

131

U. Abel and G. Arends, A remark on some combinatorial identities, General Math. 26 (2018), 35-39.

132

U. Abel and M. Ivan, A representation formula of Bernstein operators, Monatsh. Math. 188 (2019), 405-411.

https://doi.org/10.1007/s00605-018-1164-0

133

U. Abel and V. Kushnirevych, Voronovskaja type theorems for positive linear operators related to squared Bernstein polynomials, Positivity xx (201x), Published online.

https://doi.org/10.1007/s11117-018-0633-y

134

U. Abel, Wilf’s formula and a generalization of the Choi-Lee-Srivastava identities, MathLAB 2 (2019), 178-180.

135

U. Abel, A Voronovskaya-type result for simultaneous approximation by Bernstein-Chlodovsky polynomials, Result. Math. xx (2019), Online First.

DOI: 10.1007/s00025-019-1036-5

136

U. Abel, New proofs of Melzak.s identity, Aequat. Math. xx (2019), Online First.

https://doi.org/10.1007/s00010-019-00659-4

137

U. Abel, Coincidence of the barycentre and the geometric centre of weighted points, to appear in The Math. Gaz.

138

U. Abel, On the relative error between the binomial and the hypergeometric distribution, to appear in The Math. Gaz.

 

 

2001-2005 

 
1. U. Abel und M. Ivan
Die Operatoren von Bleimann, Butzer und Hahn: Alte und neue Ergebnisse in: ''Dokumentation zum 11. Rhein-Ruhr-Workshop über Angewandte Analysis, Approximationstheorie, CAGD und Numerische Mathematik (Willebadessen 16.02.-17.02.2001; ed. by G. Plonka), 6. Duisburg: Schriftenreihe des Fachbereichs Mathematik der Gerhard-Mercator-Universität SM-DU-498 (2001).
2. U. Abel und M. Ivan
Some remarks on the Bleimann, Butzer and Hahn operator (abstract), in: Abstracts of invited lectures and short communications delivered at the 10th international colloquium on numerical analysis and computer science with applications., page 1, Plovdiv, Bulgaria, August, 12-17, 2001.
3. A. Abel und U. Abel
Wie wahrscheinlich sind k Sechsen hintereinander beim mehrfachen Würfeln?, Praxis der Mathematik 43:6 (2001), 284-286.
4. U. Abel und M. Ivan
Old and new results on the operators of Bleimann, Butzer and Hahn, in: Analysis, Combinatorics and Computing, T.-X. He, P. J. S. Shiue and Zh.-K. Li (eds.), Nova Science Publ., New York, 2002, ISBN 1-59033-405-1, 1-12.
5.
U. Abel und M. Ivan
A Kantorovich variant of the Bleimann, Butzer and Hahn operators, Proceedings of the 4th international conference on functional analysis and approximation theory, Acquafredda di Maratea (Potenza), Italy, September 22.28, 2000, Vols. I and II, Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, I. Ser. 68 (2002), 205-218.
6.
U. Abel, V. Gupta und M. Ivan
The asymptotic expansion for the Baskakov-Kantorovich operators, Tiberiu Popoviciu Itinerant Seminar of Functional Equations, Approximation and Convexity, Cluj-Napoca, May 22-26, 2002, pp. 3-13.
7. U. Abel, M. Ivan und I. Rasa
Linear operators and quotients of functions, Tiberiu Popoviciu Itinerant Seminar of Functional Equations, Approximation and Convexity, Cluj-Napoca, May 22-26, 2002, pp. 15-20.
8.
U. Abel und M. Ivan
Durrmeyer variants of the Bleimann, Butzer and Hahn operators, in: Mathematical Analysis and Approximation Theory (Proc. 5th Romanian-German Seminar on Approximation Theory and its Applications, “RoGer 2002” - Sibiu; ed. by A. Lupas,, H. Gonska and L. Lupas,), Burg Verlag, Sibiu, 2002 (ISBN 973-85647-4-3), pp. 1-8.
9.
U. Abel und M. Ivan
A new proof of a Stamate mean-value theorem, Automat. Comput. Appl. Math. 11:1 (2002), 10-14.
10.
U. Abel, V. Gupta und M. Ivan
On the rate of convergence of bounded variation functions by Baskakov-Kantorovich-Bézier operators, Rev. Anal. Numér. Theor. Approx. 31:2 (2002), 123-133.
11. U. Abel und M. Ivan
The complete asymptotic expansion for the Gamma operators and their left quasi-interpolants, in: Constructive Theory of Functions, Varna 2002, B. D. Bojanov (ed.), Darba, So.a 2003, ISBN 954-90126-6-2, pp. 184-189.
12.
M. Ivan und U. Abel
A Pompeiu-type mean-value theorem and divided differences, in: Constructive Theory of Functions, Varna 2002, B. D. Bojanov (ed.), Darba, Sofia 2003, ISBN 954-90126-6-2, pp. 314-319.
13. U. Abel und M. Ivan
Asymptotic approximation of functions and their derivatives by Müller's Gamma operators, Result. Math. 43 (2003), 1-12.
14. U. Abel und M. Ivan
The complete asymptotic expansion for the left quasi-interpolants of Müller's Gamma operators, Numer. Funct. Anal. Optimization 24 (2003), 427-436.
15. U. Abel, V. Gupta und M. Ivan
On the rate of convergence of a Durrmeyer variant of the Meyer-König and Zeller operators, Arch. Inequalities and Applications 1:1 (2003), 1-10.
16. U. Abel und V. Gupta
An estimate of the rate of convergence of a Bézier variant of Baskakov-Kantorovich operators for bounded variation functions, Demonstr. Math. 36:1 (2003), 123-136.
17. U. Abel
On the Lagrange remainder of the Taylor formula, Amer. Math. Monthly 110:7 (2003), 627-633.
18. U. Abel und V. Gupta
On the rate of convergence of Bézier variant of Szász-Durrmeyer operators}, Analysis in Theory and Applications, 19:1 (2003), 81-88.
19. U. Abel, V. Gupta und M. Ivan
The complete asymptotic expansion for the Baskakov-Szász operators, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, Vol. 1 (2003), 3-15.
20. U. Abel und M. Heilmann
The complete asymptotic expansion for Bernstein-Durrmeyer operators with Jacobi weights, Mediterr. J. Math. 1 (2004), 487-499.
21. U. Abel, V. Gupta und M. Ivan
The complete asymptotic expansion for a Durrmeyer variant of the Meyer-König and Zeller operators, Math. Comp. Modelling 40 (2004), 867-875.
22. U. Abel und V. Gupta
The rate of convergence by a new type of Meyer-König and Zeller operators, Fasc. Math. 34 (2004), 15-23.
23. V. Gupta und U. Abel
Rate of convergence of bounded variation functions by a Bézier-Durrmeyer variant of the Baskakov operators, Int. J. Math. Math. Sci. 2004:9 (2004), 459-468.
24. U. Abel
Asymptotic approximation by de la Vallée Poussin means and their derivatives, J. Approx. Theory 126 (2004), 115-125.
25. U. Abel, M. Ivan und Th. Riedel
The theorem of Flett and divided differences, J. Math. Anal. Appl. 295 (2004), 1-9.
26. U. Abel und V. Gupta
Rate of convergence of Stancu beta operators for functions of bounded variation, Rev. Anal. Numér. Theor. Approx. 33:1 (2004), 3-9.
27. U. Abel und B. Della Vecchia
Enhanced asymptotic approximation by linear operators, Facta Univ., Ser. Math. Inf. 19 (2004), 37-51.
28. U. Abel, V. Gupta und M. Ivan
Rate of convergence of a Kantorovich variant of the Meyer-König and Zeller operators, Math. Inequ. Appl. 8 (2005), 135-146.
29. U. Abel, V. Gupta und R. N. Mohapatra
Local approximation by Beta operators, J. Nonlinear Anal. 62 (2005), 41-52.
30. U. Abel und M. Ivan
Asymptotic expansion of a sequence of divided differences with application to positive linear operators, J. Comp. Anal. Appl. 7 (2005), 89-101.
31. U. Abel, B. Della Vecchia und M. Ivan
Simultaneous asymptotic approximation by Jakimovski-Leviatan-Durrmeyer operators and their linear combinations, Proceedings of the 5th international conference on functional analysis and approximation theory, Acquafredda di Maratea (Potenza), Italy, June 16.23, 2004, Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, Serie II 76 (2005), 157-175.
32. U. Abel und M. Ivan
The Bleimann-Butzer-Hahn Operators. Old and Recent Results, in: Proceedings of RoGer 2004: Mathematical Analysis and Approximation Theory (2005), Mediamira Science Publisher, pp. 3-17.
33. U. Abel, V. Gupta und M. Ivan
Asymptotic approximation of functions and their derivatives by generalized Baskakov-Szász-Durrmeyer operators, Anal. Theory Appl., 21:1 (2005), 15-26.
34. U. Abel
An identity for a general class of approximation operators, J. Approx. Theory 142 (2006), 20-35.
35. U. Abel und Zh.-K. Li
A new proof of an identity of Jetter and Stöckler for multivariate Bernstein polynomials, Comput. Aided Geom. Design 23 (2006), 297-301.
36. U. Abel und M. Ivan
Enhanced asymptotic approximation and approximation of truncated functions by linear operators, in: Constructive Theory of Functions, Varna 2005, B. Bojanov (ed.), Marin Drinov Academic Publ. House, Sofia 2006, pp. 1-10.
37. M. Ivan und U. Abel
A Pompeiu-type mean-value theorem, in: Constructive Theory of Functions, Varna 2005, B. Bojanov (ed.), Marin Drinov Academic Publ. House, Sofia 2006, pp. 168-175.
38. U. Abel, M. Ivan und Zh.-K. Li
The complete asymptotic expansion for generalized Baskakov-Durrmeyer operators, erscheint demnächst in Numer. Funct. Anal. Optimization.
39. U. Abel und M. Ivan
The differential mean values of divided differences, erscheint demnächst in J. Math. Anal. Appl.
40. U. Abel und M. Ivan
A complete asymptotic expansion of power means, erscheint demnächst in J. Math. Anal. Appl.
41. U. Abel und M. Ivan
The complete asymptotic expansion for the natural quasi-interpolants of Bernstein-Durrmeyer operators, Proceedings of the international conference on numerical analysis and approximation theory (NAAT2006), Cluj-Napoca (Romania), July 5-8, zur Veröffentlichung eingereicht.
42. U. Abel und M. Ivan
On the rate of convergence of the Bleimann, Butzer and Hahn operators, zur Veröffentlichung eingereicht.