Prof. dr. Octavian Agratini

Academic degree:

Ph.D. in Mathematics (1995)

Current position:

  • Senior researcher (I) at ICTP (since December 2020)
  • Professor emeritus (since October 2nd, 2022) at the Faculty of Mathematics and Computer Science, Babes-Bolyai University

Domains of research:

  • Operator Theory (positive operators, semigroups of operators);
  • Approximation Theory (Korovkin-type approximation theory, positive approximation processes).


  • O. Agratini, Aproximare prin operatori liniari, Presa Universitară Clujeană, 2000, pp. 354, ISBN: 973-595-084-X
  • D.D. Stancu, Gh. Coman, O. Agratini, R. Trîmbiţaş, Analiză numerică şi teoria aproximării, Vol.I, Presa Universitară Clujeană, 2001, pp.414, ISBN: 973-610-043-X
  • O. Agratini, I. Chiorean, Gh. Coman, R. Trîmbiţaş, Analiză numerică şi teoria aproximării, Vol. III, Presa Universitară Clujeană, 2002, pp.551, ISBN: 973-610-164-9
  • O. Agratini, P. Blaga, Gh. Coman, Lectures on wavelets, numerical methods and statistics, Casa Cărții de Stiință, Cluj – Napoca, 2005, pp. 196, ISBN: 973-686-762-5
  • O. Agratini, A.M. Șerban, V. Ilea, Teme pentru perfecționarea profesorilor. Matematică aplicată, Vol. 5, Casa Cărții de Stiință, 2017, pp. 326, ISBN: 978-606-17-1129-1

Books on Elementary Mathematics

  • O. Agratini, S. Ursu, S. Miheţ, S., Matematici aplicate, auxiliar pentru pregătirea elevilor de liceu, Vol.I & II, Editura DACIA, Cluj – Napoca, 2001, pp.526, ISBN: 973-35-1090-4 & 973-35-1119-6
  • O. Agratini, S. Ursu, Complemente de algebră şi analiză, Editura STUDIUM Cluj-Napoca, 1998, pp. 222, ISBN: 973-9422-04-7
  • O. Agratini, M. Hudrea, S. Miheţ, S. Ursu, Matematica între plăcere şi efort, Editura STUDIUM, Cluj-Napoca, 1996, pp. 446, ISBN: 973-9258-09-3

Scientific papers published while working at ICTP


  1. O. Agratini, R. Precup, Estimates related to the iterates of positive linear operators and their multidimensional analogues. Positivity, 28 (2024), 27.
  2. O. Agratini, Properties of positive linear operators connected with squared fundamental functions, Numer. Funct. Anal. Optimiz., 45 (2024) no. 2, pp. 103-111,
  3. U. Abel and O. Agratini, On Wachnicki’s Generalization of the Gauss-Weierstrass Integral, In: Candela, A.M., Cappelletti Montano, M., Mangino, E. (eds) Recent  advances in Mathematical Analysis. Trends in Mathematics, October 2022, Birkhäuser, Cham., pp 1–13, 2023.
  4. U. Abel, O. Agratini, M. Ivan, Asymptotic properties of Kantorovich-type Szász–Mirakjan operators of higher order, Mathematical Foundations of  Computing, 2023,
  5. U. Abel, O. Agratini, Păltănea’s operators: old and new results, Bulletin of the Transilvania University of Brașov, Serie III: Mathematics and Computer Science,  3(65) (2023) no. 2, pp. 1.12,
  6. U. Abel, O. Agratini, Simultaneous approximation by Gauss–Weierstrass–Wachnicki operators, Mediterr. J. Math., 19 (2022) no. 6, art. 267,
  7. O. Agratini, R. Precup, Iterates of multidimensional approximation operators via Perov theorem, Carpathian J. Math., 38 (2022) no. 3, pp. 539-546.
  8. U. Abel, O. Agratini, On the  Durrmeyer-type variant and generalizations of Lototsky-Bernstein operators, Symmetry, 13 (2021) no. 10, Article 1841,
  9. O. Agratini, O. Dogru, Kantorovich-type operators associated with a variant of Jain operators, Stud. Univ. Babes-Bolyai Math. 66 (2021) no. 2, 279–288, doi: 10.24193/subbmath.2021.2.04 (issn)
  10. O. Agratini, S.G. Gal,  On Landau-type approximation operators, Mediterranean Journal of Mathematics, 18 (2021) art. no. 64,
  11. O. Agratini, Approximation properties of a family of integral type operators, Positivity, 25 (2021), 97–108,
  12. O. Agratini, A. Aral, Approximation of some classes of functions by Landau type operators, Results in Mathematics, 76 (2021) art. no. 12, doi: 10.1007/s00025-020-01319-9
  13. O. Agratini, Linear positive operators constructed by using Beta-type bases, Hacettepe Journal of Mathematics & Statistics,  49 (2020) no. 3, pp. 1030-1038, doi: 10.15672/hujms.549015
  14. O. Agratini, H. Karsli, Modifying an approximation process using non-Newtonian calculus, Stud. Univ. Babes-Bolyai Math. 65 (2020) no. 2, 291–301, doi: 10.24193/subbmath.2020.2.10 (issn)
  15. O. Agratini, Shift λ – invariant operators, Constructive Mathematical Analysis, 2 (2019) 3, 103-108. doi: 10.33205/cma.544094
  16. O. Agratini, From uniform to statistical convergence of binomial-type operators, In: Advances In Summability And Approximation Theory, 169 – 179, (Eds. S. A. Mohiuddine, T. Acar), Springer, Singapore, 2018. ISBN: 978-981-13-3076-6, DOI 10.1007/978-981-13-3077-3_10 (j, issn)
  17. O. Agratini, A stop over Jain operators and their generalizations, Annals of West University of Timisoara – Mathematics and Computer Science, 56 (2018) no. 2, pp. 28-42, (j, issn)

    Papers published while working at Babes-Bolyai University:
  18. O. Agratini, On a class of Bernstein-type rational functions, Numer. Funct. Anal. Optim., 41 (2020) no. 4, pp. 483-494, (j, issn)
  19. O. Agratini, Properties of discrete non-multiplicative operators, Analysis and Mathematical Physics, 9 (2020), pp. 131-141. (j, issn)
  20. O. Agratini, Approximation with arbitrary order by certain linear positive operators, Positivity, 22 (2018), pp. 1241-1254,
  21. U. Abel, O. Agratini, R. Păltănea, A complete asymptotic expansion for the quasi-interpolants of Gauss–Weierstrass operators, Mediterranean Journal of Mathematics, 15 (2018), pp. 1-10, (auth. addr.)
  22. O. Agratini, A. Aral, E. Deniz, On two classes of approximation processes of integral type, Positivity, 21 (2017), pp. 1189-1199, (issn)
  23. O. Agratini, Statistical convergence applied to Korovkin-type approximation theory, WSEAS Transactions on Mathematics, 16 (2017), pp. 183-186.
  24. O. Agratini, Kantorovich-type operators preserving affine functions, Hacettepe Journal of Mathematics and Statistics, 45 (2016) no. 6, pp. 1657-1663.
  25. U. Abel, O. Agratini, On the variation detracting property of operators of Balázs and Szabados, Acta Mathematica Hungarica, 150 (2016), pp. 383-395, (issn)
  26. U. Abel, O. Agratini, Asymptotic behaviour of Jain operators, Numerical Algorithms, 71 (2016), 553-565,
  27. O. Agratini, V. Gupta, On the uniform convergence of a q-series, Carpathian Journal of Mathematics, 32 (2016) no. 2, pp. 141-146. (issn)
  28. O. Agratini, Kantorovich sequences associated to general approximation processes, Positivity, 19 (2015), pp. 681-693.
  29. O. Agratini, A sequence of positive linear operators associated with an approximation process, Applied Mathematics and Computation, 269 (2015), pp. 23-28. (j, issn)
  30. O. Agratini, Uniform approximation of some classes of linear positive operators expressed by series, Applicable Analysis, 94 (2015) no. 8, pp. 1662-1669. (issn)
  31. O. Agratini, On a property of moduli of smoothness and K-functionals, Filomat, 29 (2015) no. 7, pp. 1425-1428. (j, issn)
  32. O. Agratini, On an approximation process of integral type, Applied Mathematics and Computation, 236 (2014), pp. 195-201. (issn, j)
  33. M. Zeng, V. Gupta, O. Agratini, Approximation by Bézier variant of the Baskakov-Kantorovich operators in the case 0<α<1, The Rocky Mountain Journal of Mathematics, 44 (2014) no. 1, pp. 317-327. (publisher, issn)
  34. O. Agratini, Approximation properties of a class of linear operators, Mathematical Methods in the Applied Sciences, 36 (2013) no. 17, pp. 2353-2358.
  35. O. Agratini, S. Tarabie, R. Trîmbiţaş, Approximation of bivariate functions by truncated classes of operators, Third International Conference on Modelling and Development of Intelligent Systems, Sibiu-Romania, October 10–12, 2013, pp. 11-19. (isbn, j)
  36. O. Agratini, On a double complex sequence of linear operators, Numerical Functional Analysis and Optimization, 34 (2013) no. 6, pp. 605-612.
  37. O. Agratini, Bivariate positive operators in polynomial weighted spaces, Abstract and Applied Analysis, 2013, art. id. 850760, (kw)
  38. O. Agratini, Statistical convergence of integral operators generated by a single kernel, Nonlinear Analysis: Theory, Methods & Applications, 75 (2012) no. 8, pp. 3465-3469, (j, issn)
  39. O. Agratini, A-statistical convergence of a class of integral operators, Applied Mathematics & Information Sciences, 6 (2012) no. 2, pp. 325-328.
  40. O. Agratini, C. Radu, On q-Baskakov-Mastroianni operators, Rocky Mountain Journal of Mathematics, 42 (2012) no. 3, pp. 773-790,
  41. O. Agratini, Statistical convergence of a non-positive approximation process, Chaos, Solitons & Fractals, 44 (2011) no. 11, pp. 977-981, (issn, j, kw)
  42. O. Agratini, C. Radu, An extension based on qR-integral for a sequence of operators, Applied Mathematics and Computation, 218 (2011) no. 1, pp. 140-147,
  43. O. Agratini, G. Nowak, On a generalization of Bleimann, Butzer and Hahn operators based on q-integers, Mathematical and Computer Modelling, 53 (2011) nos. 5-6, pp. 699-706 ,
  44. O. Agratini, An asymptotic formula for a class of approximation processes of King’s type, Studia Scientiarum Mathematicarum Hungarica, 47 (2010) no. 4, pp. 435-444. (issn)
  45. O. Agratini, On a q-analogue of Stancu operators, Cent. Eur. J. Math., 8 (2010) no. 1, pp. 191-198. DOI: 10.2478/s11533-009-0057-9 (j, issn)
  46. O. Agratini, C. Andrica, Discrete approximation processes of King’s type, Nonlinear Analysis and Variational Problems, 35 (2010), pp. 3-12.
  47. O. Agratini, O. Dogru, Weighted approximation by Szasz-King type operators, Taiwanese Journal of Mathematics, 14 (2010) no. 4, pp. 1283-1296.
  48. O. Agratini, C. Radu, Asymptotic formulae for Baskakov-Mastroianni operators based on q-integers, Supllemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, 82 (2010), pp. 195-206.
  49. O. Agratini, On statistical approximation in spaces of continuous functions, Positivity, 13 (2009), pp. 735-743.
  50. O. Agratini, On the iterates of a class of summation-type linear positive operators, Computers and Mathematics with Applications, 55 (2008) no. 6, pp. 1178-1180. (issn?)
  51. O. Agratini, On certain q-analogues of the Bernstein operators, Carpathian Journal of Mathematics, 34 (2008), pp. 281-286.
  52. O. Agratini, S. Tarabie, On approximating operators preserving certain polynomials, Automation Computer Applied Mathematics, 17 (2008) no. 2, pp.191-199.
  53. O. Agratini, Inequalities and approximation theory, in: Inequalities and Applications, eds.: Themistocles M. Rassias, Dorin Andrica, pp. 1-12, Cluj University Press, 2008, ISBN ????
  54. O. Agratini, On a class of linear positive bivariate operators of King type, Studia Universitatis Babes-Bolyai, Mathematica, 51 (2006) no. 4, pp. 13-22.
  55. O. Agratini, On the variation detracting property of a class of operators, Applied Mathematics Letters, 19 (2006) no. 11, pp. 1261-1264.
  56. O. Agratini, On approximation of functions by positive linear operators, Stud. Cercet. Stiint. Ser. Mat, Proceedings of ICMI 45 (2006), pp. 17-28. (jurnal?)
  57. O. Agratini, Linear operators that preserve some test functions, International Journal of Mathematics and Mathematical Sciences 2006, ID 94136, pp. 1-11. (kw?, issn?)
  58. O. Agratini, Quantitative approximations by using scaling type functions, Studia Universitatis Babes-Bolyai Mathematica, 50 (2005) no. 2, pp. 3-13.
  59. O. Agratini, On the rate of convergence of some integral operators for functions of bounded variation, Studia Scientiarum Mathematicarum Hungarica, 42 (2005) no. 2, pp. 235-252,
  60. O. Agratini, Rate of convergence of a class of Bézier type operators for functions of bounded variation, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, 76 (2005), pp. 177-195.
  61. O. Agratini, A generalization of Durrmeyer-type polynomials and their approximation, Applications of Fibonacci Numbers, Proceedings of the tenth international research conference on Fibonacci numbers and their applications, 9 (2004), pp. 9-18. (abstract, kw)
  62. O. Agratini, B. Della Vecchia, Mastroianni operators revisited, Facta Universitatis, Nis, Series: Mathematics and Informatics, 19 (2004), pp. 53-63. (kw?)
  63. O. Agratini, Linear operators generated by a probability density function, In: Advances in Constructive Approximation: Vanderbilt 2003, Proceedings of the international conference, Nashville, TN, USA, May 14–17, 2003. Brentwood, TN: Nashboro Press (ISBN 0-9728482-2-3/hbk). Modern Methods in Mathematics, Eds. M. Neamtu and E. B. Saff, (2004), pp. 1-12. (kw)
  64. O. Agratini, On the convergence of a truncated class of operators, Bulletin of the Institute of Mathematics Academia Sinica, 31 (2003) no. 3, pp. 213-223.
  65. O. Agratini, On some Bernstein type operators: iterates and generalizations, East Journal on Approximations, 9 (2003) no. 4, pp. 415-426. (issn?)
  66. O. Agratini, I.A. Rus, Iterates of some bivariate approximation process via weakly Picard operators, Nonlinear Analysis Forum, 8 (2003), pp. 159-168. (issn?)
  67. O. Agratini, I.A. Rus, Iterates of a class of discrete linear operators via contraction principle, Commentationes Mathematicae Universitatis Carolinae, 44 (2003) no. 3, pp. 555-563. (issn?)
  68. O. Agratini, Operators generated by a quasi-scaling type function, Revista de la Union Matematica Argentina, 44 (2003) no. 2, pp. 21-30.
  69. O. Agratini, On approximation properties of Balázs-Szabados operators their Kantorovich extension, Korean Journal of Computational & Applied Mathematics, 9 (2002), pp. 361-372.
  70. O. Agratini, Stancu modified operators revisited, Revue d’Analyse Numerique et de Theorie de l’Approximation, 31 (2002) no. 1, pp. 9-16.
  71. O. Agratini, Approximation operators – solutions and questions, Seminaire de la Theorie de La Meilleure Approximation, Convexite Et Optimisation, Cluj- Napoca, 22-26 mai, 2002, Editura SRIMA (kw?)
  72. O. Agratini, On some wavelet type linear operators, Proceedings of the International Symposium on Numerical Analysis and Approximation Theory, Cluj-Napoca, May 9-11, 2002, pp. 46-53. (kw?)
  73. O. Agratini, The mysterious wavelets world, Poceedings of the 5th Romanian-German Seminar on Mathematical Analysis and Approximation Theory, Sibiu, June 2002, pp. 9-35. (kw?)
  74. O. Agratini, On some operators of discrete type, Supllemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, Proceedings of the 4th International Conference on Functional Analysis and Approximation Theory, Acquafredda di Maratea, (Potenza-Italy), 68 (2000), pp. 229-243. (kw)
  75. O. Agratini, On the rate of convergence for semigroups and processes of Feller type, Analele Universitatii Bucuresti, Matematica-Informatica, 51 (2002) no. 1, pp. 3-11.
  76. O. Agratini, Binomial polynomials and their applications in Approximation Theory, Conferenze del Seminario di Matematica dell Universita di Bari, 281 (2001), 1-22. (kw?)
  77. O. Agratini, Korovkin type error estimates for Meyer-Konig and Zeller operators, Mathematical Inequalities and Applications, 4 (2001), 119-126. (kw)
  78. O. Agratini, An approximation process of Kantorovich type, Miskolc Mathematical Notes, 2 (2001) no. 1, 3-10.
  79. O. Agratini, On a certain class of approximation operators, Pure Mathematics and Applications, 11 (2000) no. 2, pp. 119-127. (kw, j., issn)
  80. O. Agratini, On the rate of convergence of a positive approximation process, Nihonkai Mathematical Journal, 11 (2000) no. 1, pp. 47-56. (kw)
  81. O. Agratini, Application of Popoviciu’s high convexity to the study of some sequences properties, Seminaire de la Theorie de la Meilleure Approximation, Convexite et Optimisation Cluj-Napoca, 26-29 octobre, 2000, pp. 1-15. (kw)
  82. O. Agratini, More than a summing up about Meyer-Konig and Zeller operators, Proceedings of the 4th Romanian-German Seminar on Approximation Theory and its Applications, Brasov, 3-5 July, 2000, pp.13-25, Duisburg: Schriftenreihe des Fachbereichs der Gerhard-Mercator-Universitat, SM-DU-48 (abstract, kw)
  83. O. Agratini, Properties concerning the Baskakov-Beta operators, in: Analysis, Functional Equations, Approximation and Convexity, Proceedings of the Conference held in honour of Professor Elena Popoviciu on the occasion of her 75th birthday, Editura Carpatica, pp. 1-7, 1999. (kw)
  84. O. Agratini, Note on a class of operators on infinite interval, Demonstratio Mathematica, 32 (1999) no. 4, pp. 789-794. (abstract, kw)
  85. O. Agratini, On a sequence of linear and positive operators, Facta Universitatis, Nis, Series: Mathematics and Informatics, 14 (1999), pp. 41-48. (kw?)
  86. O. Agratini, Approximation properties of a class of linear operators, Buletinul Academiei de Științe a Republicii Moldova, Matematica, 29 (1999) no. 1, pp. 73-78. (kw?)
  87. O. Agratini, Smoothness properties of positive summation integral operators, East Journal on approximation, 5 (1999) no. 4, pp. 381-392. (kw?)
  88. O. Agratini, An asymptotic property of integral type operators, Mathematica, 40 (63) (1998), pp. 3-8. (abstr, kw)
  89. O. Agratini, On a problem of A. Lupaş, General Mathematics, 6 (1998), pp. 3-10. (abstract, kw, refs)
  90. O. Agratini, Asymptotic formulae for recursively defined Baskakov-type operators, Publications de L’Institut Mathematique (Beograd) (NS), 63 (1998) no. 77, pp. 152-162. (ISSN)
  91. O. Agratini, Properties of a new class of recursively defined Baskakov-type operators, Archivum Mathematicum, 34 (1998) no. 3, pp. 353-359.
  92. O. Agratini, Approximation properties of a generalization of Bleimann, Butzer and Hahn operators, Mathematica Pannonica, 9 (1998), pp. 165-171.
  93. O. Agratini, Linear combinations of D.D. Stancu polynomials, Revue d’Analyse Numerique et de Theorie de l’Approximation, 27 (1998) no. 1, 15-22.
  94. O. Agratini, Construction of Baskakov-type operators by wavelets, Revue d’Analyse Numerique et de Theorie de l’Approximation, 26 (1997) nos. 1-2, pp. 3-11.
  95. O. Agratini, On a functional equation, Studia Universitatis Babes-Bolyai Mathematica, 42 (1997) no. 4, pp. 1-8.
  96. O. Agratini, A bivariate extension of the Bernstein polynomials, Studia Universitatis Babes-Bolyai Mathematica, 42 (1997) no. 2, pp. 5-8.
  97. O. Agratini, On modified Beta operators, Studia Universitatis Babes-Bolyai Mathematica, 42 (1997) no. 1, pp. 5-9.
  98. O. Agratini, On a class of linear approximating operators, Mathematica Balkanica N.S., 11 (1997) nos. 3-4, pp. 407-412. (kw)
  99. O. Agratini, On simultaneous approximation by Stancu-Bernstein operators, Approximation and Optimization, Proceedings of ICAOR International Conference, 1997, ISBN 973-98180-7-2, pp. 157-162. (abstr)
  100. O. Agratini, Application of divided differences to the study of monotonicity of a sequence of D.D. Stancu polynomials, Revue d’Analyse Numerique et de Theorie de l’Approximation, 25 (1996) nos. 1-2, pp. 3-10. (kw)
  101. O. Agratini, A class of Bleimann, Butzer and Hahn type operators, Analele Universitatii din Timisoara, 34 (1996) no. 2, 173-180.
  102. O. Agratini, On the monotonicity of a sequence of Stancu-Bernstein type operators, Studia Univ. ”Babeș-Bolyai”, Mathematica, vol. 41 (XLI), fasc.2,1996, pp.17-23. (to do: kw, link Studia)
  103. O. Agratini, Approximation theorem in Lp for a class of operators constructed  by wavelets, Studia Univ. ”Babeș-Bolyai”, Mathematica, 41 (1996) no. 4, pp. 11-16. (to do: link Studia)
  104. O. Agratini, An application of divided differences, Technical University of Cluj-Napoca, Automation Computers Applied Mathematics, Scientific Journal, 4 (1995) no. 2, pp. 95-99.
  105. O. Agratini, Approximation properties of a class of operators of Stancu-Kantorovich type, Research Seminar on Numerical and Statistical Calculus, “Babeş-Bolyai” Univ., Cluj-Napoca, 1 (1994), pp. 3-12. (kw)
  106. O. Agratini, On the construction of approximating linear positive operators by probabilistic methods, Studia Univ. ”Babeș-Bolyai”, Mathematica, 38 (1993) no. 4, pp. 45-50. (to do: kw, link studia)

Other papers

Papers on Elementary Mathematics

  • O. Agratini, Asupra noțiunii de convergență statistică, Didactica Mathematica, Vol. 32, 2014, 1-8.
  • O. Agratini, C. Radu, On some probability problems, Didactica Mathematica, Vol. 26, 2008, No. 1, 1-8.
  • O. Agratini, Aplicaţii practice ale ecuaţiilor diferenţiale, Lucrările Seminarului Didactica Mathematicii, Vol. 17, 2001, 5-14.
  • O. Agratini, Proprietăţile şirurilor Fibonacci şi Lucas, Lucrările Seminarului Didactica Mathematicii, Vol. 16, 2000, 3-14.
  • O. Agratini, Asupra proprietăţilor funcţiilor euleriene, Lucrările Seminarului Didactica Mathematicii, Vol. 14, 1998, 17-26.
  • O. Agratini, Probabilistic and non-probabilistic properties of the sequence {Wn}, Lucrările Seminarului Didactica Mathematicii, Vol. 12, 1996, 1-6.
  • O. Agratini, Consideration upon a contest problem, Lucrările Seminarului Didactica Mathematicii, Vol. 11, 1995, 19-22.
  • O. Agratini, Notă asupra tratării unor probleme de teoria probabilităţilor, Lucrările Seminarului Didactica Mathematicii, Vol. 8, 1992, 1-4.
  • O. Agratini, Aplicaţii ale transformărilor geometrice, Lucrările Seminarului Didactica Mathematicii, Vol. 6, 1990, 21-26.

Version of June 6, 2024.