Summary

Prof. dr. Costică Mustăţa – outstanding member of the Institute, at present honorary member.

He was employed at the Institute between 1968-2013, and he served as Secretary of the Scientific Council.

He is a member of the Cluj Team on Numerical Analysis and Approximation Theory.

At present, he serves as a member of the Editorial Board of Journal of Numerical Analysis and Approximation Theory, edited under the auspices of the Romanian Academy, and of the (ISI ranked) journal Carpathian Journal of Mathematics.


Version of July 16, 2017.

 

In Romanian:

Membru marcant al Institutului (în prezent, membru de onoare).

A fost angajat la Institut în perioada 1968-2013, unde a fost membru al Consiliului Ştiinţific.

In prezent este membru al colectivului de redactie al revistei de specialitate Journal of Numerical Analysis and Approximation Theory, editata sub egida Academiei Romane, precum si la Carpathian Journal of Mathematics (jurnal ISI).

CV

Personal Data

Date and place of birth 11 June 1942
Băileşti, district Dolj
Romania

Education and degrees

1975 Ph.D. in Mathematics, University Babeş-Bolyai, Cluj-Napoca
Scientific advisor: Prof. Dr. Elena Popoviciu
Thesis “The best approximation of the functions with given behavior”
1963-1968 Batchelor Degree, Mathematics
University Babeş-Bolyai, Cluj-Napoca
1953-1956 High school Băileşti, district Dolj

Employment history

1968-1971 Research assistant at Tiberiu Popoviciu Institute of Numerical Analysis
1971-1979 Researcher at Tiberiu Popoviciu Institute of Numerical Analysis
1979-1990 Senior researcher (III) at Tiberiu Popoviciu Institute of Numerical Analysis
1990-1994 Senior researcher (II) at Tiberiu Popoviciu Institute of Numerical Analysis
1998-2004 Associate Professor at North University of Baia-Mare
1994-2013 Senior researcher (I) at Tiberiu Popoviciu Institute of Numerical Analysis

Editorial activities

Recent research domains

  • Approximation and best approximation in function spaces and abstract spaces
  • Theorems of extension and relationship with problems of best approximation
  • Existence and study of properties for selections associated to metric projections

Past research activity:

  • Approximation by linear and positive operators
  • Approximation of solutions of boundary problems for differential equations
  • Spline functions and applications
  • M-ideals in metric spaces

Grants

  1. GAR nr.4122GR/1998,1990 cu MCT, Theme: Appromaximations of the solutions for PDE by means of spline functionms and wavelets. (coordinatortor).
  2. GAR nr.6100GR/2000 cu ANSTI, Theme: Numerical mathods for solving boundary problems for ODE and PDE (cooordinator).
  3. GAR nr.65/2001 of the Romanian Academy, Theme: The unknown incremental method applied to diffusion-convection problems (coordinator)
  4. GAR nr.46/2002 of the Romanian Academy, Theme: The unknown incremental method applied to diffusion-convection problems (coordinator)
  5. GAR no.15/2003 of the Romanian Academy
  6. GAR no.13/2004 of the Romanian Academy

Other professional activities

  • Scientific secretary at Tiberiu Popoviciu Institute of Numerical Analysis
  • Reviewer at “Zentralblatt fur Mathematik” and “Mathematical Reviews”.
  • Member in the Expert Committee of CNCSIS.

Didactic activity

  • Linear algebra and analytical geometry
  • Functional analysis
  • The best approximation
  • Operators theory
  • Applied mathematics in economy
Publications

Books

  1. C. Mustăţa, M. Bărbosu, Algebra, analytic geometry and tensorial calculus. Editura Dacia, Cluj-Napoca, Chapters I and II, pp. 9-127, 2000.
  2. C. Mustăţa, I. Taşcu, Applied mathematics in economy, RISOPRINT Publishing House, Cluj-Napoca, 2004.

Articles

  1. C. Mustăța, Sandwich theorems for radiant functions, J. Numer. Anal. Approx. Theory, 44 (2015) no. 1, 81-90.
  2. C. Mustăţa, On the extensions preserving the shape of semi-Holder function, Results Math. 63 (2013), 425-433.
  3. C. Mustăţa, On the existence and uniqueness of extensions of semi-Holder real-valued functions, Rev. Anal. Numer. Theor. Approx., 39 (2010) no. 2, 134-140.
  4. C. Mustăţa, Extensions of semi-Hölder real valued functions on a quasi-metric space, Rev. Anal. Numer. Theor. Approx., 38 (2009), no. 2, pp. 164-169.
  5. C. Mustăţa, On the approximation of the global extremum of a semi-Lipschitz function, Mediterr. J. Math. 6 (2009), pp. 169-180.
  6. C. Mustăţa, Asupra extensiei si aproximarii functiilor semi-Lipschitz reale, Seminarul Tiberiu Popoviciu de Ecuatii Functionale, Aproximare si convexitate, 24 – 27 septembrie 2008, Cluj-Napoca, pp. 25-29.
  7. C. Mustăţa, On a theorem of Baire about lower semi-continuous functions, Rev. Anal. Numer. Theor. Approx. 37 (2008) no. 1, 71-75.
  8. C. Mustăţa, Best uniform approximation of a bounded function by extensions of semi-Lipschitz functions, Annals of the Tiberiu Popoviciu Seminar of Functional Equations Approximation and Convexity, vol. 5, 2007, 87-98.
  9. C. Mustăţa, Extension and approximation of semi-Lipschitz functions, Analele Univ. De Vest Timişoara, Seria Matematică-Informatică XLV, 2 (2007), 83-92.
  10. C. Mustăţa, Best uniform approximation of semi-Lipschitz function by extension, Rev. Anal. Numér. Théor. Approx. 36 (2007) 2, pp. 161-171.
  11. C. Mustăţa, On the converses of the reduction principle in inner product spaces, Studia Univ. Babeş-Bolyai, Mathematica, vol LI  (2006) no. 3, 97-104.
  12. S. Cobzas, C. Mustăţa, Best approximation in spaces with asymmetric norm, Rev. Anal. Numer. Theor. Approx. 35 (2006) no. 1, 17-31.
  13. C. Mustăţa, On the extension of semi-Lipschitz functions on asymmetric normed spaces, Rev. Anal. Numer. Theor. Approx. 34 (2005) no.2 , 139-150.
  14. C. Mustăţa, On the characterization of generalized nearest point, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, vol. 2 (2004), 65-74.
  15. C. Mustăţa, Characterization of ε-nearest points in space with asymmetric seminorm, Rev. Anal. Numer. Theor. Approx. 33 (2004) no. 2, 203-208.
  16. C. Mustăţa and Şt. Cobzaş, Extension of bounded linear functionals and best approximation in space with asymmetric norm, Rev. Anal. Numer. Theor. Approx.. 33 (2004) no. 1, 39-50.
  17. C. Mustăţa, On the uniqueness of extension and unique best approximation in the dual of an asymmetric normed linear space, Rev. Anal. Numer. Theor. Approx. 32 (2003) no. 2, 187-192.
  18. C. Mustăţa, A Phelps type result for spaces with asymmetric norms, Bul. Şt. Univ. Baia Mare, Seria B, Fascicola matematică-informatică, 18 (2002) no. 2, 275-280.
  19. C. Mustăţa, On the extremal semi-Lipschitz function, Rev. Anal. Numer. Theor. Approx. 31 (2002) Nr. 1, 103-108.
  20. C. Mustăţa, Extension and approximation of semi-Lipschitz functions on quasi-metric linear spaces, Proceedings of the International Symposium on Numerical Analysis and Approximation Theory 9-11 May 2002, 362-385.
  21. C. Mustăţa, Extension of convex semi-Lipschitz Functions on quasi-metric linear spaces, Seminaire de la Théorie de la Meilleure Approximation, Convexité et Optimization, Cluj-Napoca, 29 November 2001, 85-92.
  22. C. Mustăţa, Extension of starshaped bounded semi-Lipschitz function on a quasi metric linear spaces. ”135-th Pannonian Applied Mathematical Meeting” 4-7 oct. 2001, 285-291.
  23. C. Mustăţa, Extension of semi Lipschitz function on quasi-metric spaces, Rev. Anal. Numer. Theor. Approx. 30 (2001) nr. 1, 61-67.
  24. C. Mustăţa, Uniqueness of extension of semi-Lipschitz functions on quasi-metric spaces, Bul. Ştiinţ. Univ. Baia Mare, Seria B, Fascicola matematică-informatică, 16 (2000) no. 2, pp. 207-212.
  25. C. Mustăţa, Some remarks concerning norm preserving extension and best approximation, Rev. Anal. Numer. Theor. Approx., 29 (2000) No. 2, pp. 173-180.
  26. C. Mustăţa, Şt. Cobzaş, Extension of Lipschitz functions and best approximation, in ”Research on Theory of Allure, Approximation, Convexity and Optimization, SRIMA, Cluj-Napoca, (1999), 3-21.
  27. C. Mustăţa, The approximation by spline functions of the solution of a polylocal problem for a differential equation of order p, ”Conference on Analysis, Functional Equations, Approximation and Convexity”, Cluj-Napoca, October 15-16, (1999), 197-201.
  28. C. Mustăţa, On a problem of B.A. Karpilovskaya, Rev. Anal. Numér. Théor. Approx. 29 (1999) no. 2, pp. 179-189.
  29. A.C. Mureşan, C. Mustăţa, A Galerkin Methods for a singularly perturbed bilocal problem, Bull. Şt. Univ. Baia Mare, Seria B, Fascicola Matematică-informatică, 15 (1999) nos. 1-2, 89-102.
  30. C. Mustăţa, On the derivative-interpolating spline functions of even degree, Bull. Şt. Univ. Baia Mare, Seria B, Fascicola Matematică-informatică, 14 (1998) no. 1, 51-58.
  31. C. Mustăţa, Şt. Cobzaş, Extension of bilinear functionals and best approximation in 2-normed space, Studia Univ. ”Babeş-Bolyai”, Seria Mathematica, XLIII, Nr.2 (1998), 1-13.
  32. C. Mustăţa, A. Mureşan and R. Mustăţa, The approximation by spline functions of the solutions of a singularly perturbed bilocal problem, Rev. Anal. Numér. Théor. Approx. 27 (1998).
  33. C. Mustăţa, Approximation by spline functions of the solutions of a linear bilocal problem, Rev. Anal. Numér. Théor. Approx. 26 (1997) 1-2. 137-148.
  34. C. Mustăţa, Şt. Cobzaş, Extension of bilinear operators and best approximation in 2-normed spaces, Rev. Anal. Numér. Théor. Approx., 25 (1996) nos. 1-2, 63-75.
  35. C. Mustăţa, On the metric projection and the quotient mapping, Rev. Anal. Numér. Théor. Approx., 24 (1995) nos. 1-2, 191-199.
  36. C. Mustăţa, Şt. Cobzaş, Selections associated to the metric projection, Rev. Anal. Numér. Théor. Approx., 24 (1995) nos. 1-2, 45-52.
  37. C. Mustăţa, On the selections associated to the metric projection, Rev. Anal. Numér. Théor. Approx. 23 (1994) 1, 89-93 (MR # 96b: 46019).
  38. C. Mustăţa, Common selections for the metric projections, Mathematica 35 (58) (1993) 2, 193-200 (MR # 96b: 46018).
  39. C. Mustăţa, Selections with values Bernstein polynomials associated to the extension operator for Lipschitz functions, Rev. Anal. Numér. Théor. Approx. 22 (1993) 2, 207-216 (MR # 96k: 41047).
  40. C. Mustăţa, On a contest problem, Lucrările Seminarului ”Didactica Matematicii”, vol. 8 (1992), 123-128 (in Romanian).
  41. C. Mustăţa, Selections associated to McShane’s extension theorem for Lipschitz functions, Rev. Anal. Numér. Théor. Approx. 21 (1992) 2, 135-145 (MR # 94h: 46008).
  42. C. Mustăţa, On a problem of extremum, ”Babeş-Bolyai” Univ., Research Seminars, Seminar on Mathematical Analysis, Preprint nr.7 (1991), 87-93 (MR # 94a: 26007).
  43. C. Mustăţa, Extension of Hölder functions and some related problems of best approximation, ”Babeş-Bolyai” Univ., Research Seminars, Seminar on Mathematical Analysis, Preprint nr. 7 (1991), 71-86 (MR # 94f: 41038).
  44. C. Mustăţa, An application of a theorem of McShane, Seminar on Functional Analysis and Numerical Methods, Preprint Nr. 1 (1989), 75-84 (MR # 91j: 54024).
  45. C. Mustăţa, D. Andrica, An abstract Korovkin type theorem and applications, Studia Univ. ”Babeş-Bolyai” XXXIV, fasc. 2 (1989), 44-41 (MR # 91j: 41043).
  46. C. Mustăţa, M-ideals in metric spaces, ”Babeş-Bolyai” University, Faculty of Math. and Physics, Research Seminars, Seminar on Mathematica Analysis, Preprint Nr.7 (1988), 67-74 (MR # 90b: 54019).
  47. C. Mustăţa, C. Iancu, Error estimation in the approximation of function by interpolation cubic splines, Mathematica 29 (52) 1 (1987), 33-39 (MR # 89f: 41012).
  48. C. Mustăţa, On the exactity of the error evaluation in the approximation by cubic spline of interpolation, ”Babeş-Bolyai” University, Faculty of Math. and Physics, Research Seminars, Seminar on Functional Analysis and Numerical Methods, Preprint Nr. 1 (1987), 93-102 (MR # 977080).
  49. C. Mustăţa, On the uniqueness of extension of Lipschitz odd functions, ”Babeş-Bolyai” University, Seminar on Optimization Theory, Report Nr. 8 (1987), 75-80 (MR # 90c: 41069).
  50. C. Mustăţa, On the extension of Lipschitz functions, Seminar of Funct. Analysis and Numerical Methods, Preprint Nr. 1 (1986), 83-92.
  51. C. Mustăţa, On the extension of Hölder functions, Seminar of Functional Analysis and Numerical Methods, Preprint Nr. 1 (1985), 85-92 (MR # 87h: 46068).
  52. C. Mustăţa, On a surjectivity theorem, Seminar of Functional Analysis and Numerical Methods, Preprint Nr. 1, (1985), 73-84 (MR # 832505).
  53. C. Mustăţa, About the determination of extremes of Hölder functions, Seminar of Functional Analysis and Numerical Methods, Preprint Nr. 1 (1983), 107-116.
  54. C. Mustăţa, On the extension problem with prescribed norm, Seminar Funct. Anal. and Num. Methods, Preprint Nr. 4 (1981), 93-99 (MR # 84f: 46027).
  55. C. Mustăţa, Extension of bounded Lipschitz functions and some related problems of best approximation, Seminar of Functional Analysis and Numerical Methods, Preprint Nr. 1 (1980), 1-22 (MR # 84h: 54017).
  56. C. Mustăţa, On the uniqueness of the extension of real Hölder functions, Sem. Itinerant de Ecuaţii Funcţionale, Aproximare şi Convexitate, 1980, Cluj-Napoca, 91-96 (in Romanian).
  57. C. Mustăţa, The extension of starshaped bounded Lipschitz functions, Anal. Numer. Théor. Approx. 9 (1980) 1, 93-99.
  58. C. Mustăţa, Şt. Cobzaş, Norm preserving extension of convex Lipschitz functions, J. Approx. Theory 24 (1978) no. 3, 238-244 (MR # 82j: 41034).
  59. C. Mustăţa, A characterization of semichebyshevian sets in a metric space, Mathematica – Revue Anal. Num. Theor. Approx., L’Analyse Numérique Théor. Approx. 7 (1978) 2, 169-170 (MR # 80g: 41014).
  60. C. Mustăţa, Best approximation and unique extension of Lipschitz functions, J. Approx. Theory 19 (1977) no. 3, 222-230 (MR 55 # 6086).
  61. C. Mustăţa, Norm preserving extension of starshaped Lipschitz functions, Mathematica 19 (42) 2 (1977), 183-187 (MR # 80c: 46031).
  62. C. Mustăţa, A characterization of Chebyshevian subspaces of annihilator-type, Mathematica – Rev. Anal. Numér. Théor. Approx., L’Analyse Numérique et la Théorie de l’Approx. 6 (1977) 1, 51-56 (MR 58 # 29722).
  63. C. Mustăţa, On the best approximation in metric spaces, Mathematica – Rev. Anal. Numer. Theor. Approx., L’Analyse Numer. et la Théorie de l’Approximation 4 (1975) 1, 45-50 (MR # 82c: 46052).
  64. C. Mustăţa, A monotony property of the best approximation operator in the space of Lipschitz functions, Rev. Anal. Numer. Teoria Approximatiei 3 (1974) 2, 153-160 (MR57 # 6945) (in Romanian).
  65. C. Mustăţa, A classification of Lipschitz functions, Rev. Anal. Num. Theor. Approx. 3 (1974) 1, 107-111 (MR 52 #670) (in Romanian).
  66. C. Mustăţa, Gh. Lupu, Consideration on the ”equilibrium” electrons distribution function for a homogeneous high frequency, fully ionized plasma, Rev. Roumaine de Physique 18 (1973) 3, 365-372.
  67. C. Mustăţa, On the uniqueness of the extension of continuous p-seminorms, Rev. Anal. Numer. Teoria Approximatiei 2 (1973) no. 2, 173-177 (MR 53 # 8759) (in Romanian).
  68. C. Mustăţa, On the Chebyshev subspaces in normal space of Lipschitz functions, Rev. Anal. Numer. Teoria Approximatiei, 2 (1973) no. 1, 81-87 (MR 52 # 8758) (in Romanian).

PhD Thesis

  • The best approximation of the functions with given behavior, Scientific advisor Prof. Dr. Elena Popoviciu, University Babeş-Bolyai, Cluj-Napoca, 1975.

Other works

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