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On the Korovkin-type approximation of set-valued continuous functions

Yıl 2021, Cilt: 4 Sayı: 1, 119 - 134, 01.03.2021
https://doi.org/10.33205/cma.863145

Öz

This paper is devoted to some Korovkin approximation results in cones of Hausdorff continuous set-valued functions and in spaces of vector valued functions. Some classical results are exposed in order to give a more complete treatment of the subject. New contributions are concerned both with the general theory than in particular with the so-called convexity monotone operators, which are considered in cones of set-valued function and also in spaces of vector-valued functions.

Teşekkür

Work performed under the auspices of G.N.A.M.P.A. (INdAM)

Kaynakça

  • F. Altomare, M. Campiti: Korovkin-type Approximation Theory and Its Applications, De Gruyter Studies in Mathematics 17, Berlin-Heidelberg-New York, (1994).
  • F. Altomare, M. Cappelletti, V. Leonessa and I. Ra¸sa: Markov Operators, Positive Semigroups and Approximation Processes, De Gruyter Studies in Mathematics 61, Berlin-Munich-Boston, (2015).
  • H. Berens, G. G. Lorentz: Geometric theory of Korovkin sets, J. Approx. Theory, 15 (3) (1975), 161–189.
  • M. Campiti: A Korovkin-type theorem for set-valued Hausdorff continuous functions, Le Mathematiche, 42 (I–II) (1987), 29–35.
  • M. Campiti: Approximation of continuous set-valued functions in Fréchet spaces I, Rev. Anal. Numér. Théor. Approx., 20 (1–2) (1991), 15–23.
  • M. Campiti: Approximation of continuous set-valued functions in Fréchet spaces II, Rev. Anal. Numér. Théor. Approx., 20 (1–2) (1991), 24–38.
  • M. Campiti: Korovkin theorems for vector-valued continuous functions, in "Approximation Theory, Spline Functions and Applications" (Internat. Conf., Maratea, May 1991), 293–302, Nato Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 356, Kluwer Acad. Publ., Dordrecht, 1992.
  • M. Campiti: Convergence of nets of monotone operators between cones of set-valued functions, Atti dell’Accademia delle Scienze di Torino, 126 (1992), 39–54.
  • M. Campiti: Convexity-monotone operators in Korovkin theory, Rend. Circ. Mat. Palermo, 33 (1993), 229–238.
  • M. Campiti: Korovkin-type approximation in spaces of vector-valued and set-valued functions, Applicable Analysis, 98 (13) (2019), 2486–2496.
  • L. B. O. Ferguson, M. D. Rusk: Korovkin sets for an operator on a space of continuous functions, Pacific J. Math., 65 (2) (1976), 337–345.
  • W. Heping: Korovkin-type theorem and application, J. Approx. Theory, 132 (2005), 258–264.
  • K. Keimel, W. Roth: A Korovkin type approximation theorem for set-valued functions, Proc. Amer. Math. Soc., 104 (1988), 819–824.
  • K. Keimel, W. Roth: Ordered cones and approximation, Lecture Notes in Mathematics, 1517, Springer-Verlag Berlin Heidelberg, (1992).
  • N. I. Mahmudov: Korovkin-type theorems and applications, Cent. Eur. J. Math., 7 (2) (2009), 348–356.
  • T. Nishishiraho: Convergence of quasi-positive linear operators, Atti Sem. Mat. Fis. Univ. Modena, 29 (1991), 367–374.
Yıl 2021, Cilt: 4 Sayı: 1, 119 - 134, 01.03.2021
https://doi.org/10.33205/cma.863145

Öz

Kaynakça

  • F. Altomare, M. Campiti: Korovkin-type Approximation Theory and Its Applications, De Gruyter Studies in Mathematics 17, Berlin-Heidelberg-New York, (1994).
  • F. Altomare, M. Cappelletti, V. Leonessa and I. Ra¸sa: Markov Operators, Positive Semigroups and Approximation Processes, De Gruyter Studies in Mathematics 61, Berlin-Munich-Boston, (2015).
  • H. Berens, G. G. Lorentz: Geometric theory of Korovkin sets, J. Approx. Theory, 15 (3) (1975), 161–189.
  • M. Campiti: A Korovkin-type theorem for set-valued Hausdorff continuous functions, Le Mathematiche, 42 (I–II) (1987), 29–35.
  • M. Campiti: Approximation of continuous set-valued functions in Fréchet spaces I, Rev. Anal. Numér. Théor. Approx., 20 (1–2) (1991), 15–23.
  • M. Campiti: Approximation of continuous set-valued functions in Fréchet spaces II, Rev. Anal. Numér. Théor. Approx., 20 (1–2) (1991), 24–38.
  • M. Campiti: Korovkin theorems for vector-valued continuous functions, in "Approximation Theory, Spline Functions and Applications" (Internat. Conf., Maratea, May 1991), 293–302, Nato Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 356, Kluwer Acad. Publ., Dordrecht, 1992.
  • M. Campiti: Convergence of nets of monotone operators between cones of set-valued functions, Atti dell’Accademia delle Scienze di Torino, 126 (1992), 39–54.
  • M. Campiti: Convexity-monotone operators in Korovkin theory, Rend. Circ. Mat. Palermo, 33 (1993), 229–238.
  • M. Campiti: Korovkin-type approximation in spaces of vector-valued and set-valued functions, Applicable Analysis, 98 (13) (2019), 2486–2496.
  • L. B. O. Ferguson, M. D. Rusk: Korovkin sets for an operator on a space of continuous functions, Pacific J. Math., 65 (2) (1976), 337–345.
  • W. Heping: Korovkin-type theorem and application, J. Approx. Theory, 132 (2005), 258–264.
  • K. Keimel, W. Roth: A Korovkin type approximation theorem for set-valued functions, Proc. Amer. Math. Soc., 104 (1988), 819–824.
  • K. Keimel, W. Roth: Ordered cones and approximation, Lecture Notes in Mathematics, 1517, Springer-Verlag Berlin Heidelberg, (1992).
  • N. I. Mahmudov: Korovkin-type theorems and applications, Cent. Eur. J. Math., 7 (2) (2009), 348–356.
  • T. Nishishiraho: Convergence of quasi-positive linear operators, Atti Sem. Mat. Fis. Univ. Modena, 29 (1991), 367–374.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Michele Campıtı 0000-0003-3794-1878

Yayımlanma Tarihi 1 Mart 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 1

Kaynak Göster

APA Campıtı, M. (2021). On the Korovkin-type approximation of set-valued continuous functions. Constructive Mathematical Analysis, 4(1), 119-134. https://doi.org/10.33205/cma.863145
AMA Campıtı M. On the Korovkin-type approximation of set-valued continuous functions. CMA. Mart 2021;4(1):119-134. doi:10.33205/cma.863145
Chicago Campıtı, Michele. “On the Korovkin-Type Approximation of Set-Valued Continuous Functions”. Constructive Mathematical Analysis 4, sy. 1 (Mart 2021): 119-34. https://doi.org/10.33205/cma.863145.
EndNote Campıtı M (01 Mart 2021) On the Korovkin-type approximation of set-valued continuous functions. Constructive Mathematical Analysis 4 1 119–134.
IEEE M. Campıtı, “On the Korovkin-type approximation of set-valued continuous functions”, CMA, c. 4, sy. 1, ss. 119–134, 2021, doi: 10.33205/cma.863145.
ISNAD Campıtı, Michele. “On the Korovkin-Type Approximation of Set-Valued Continuous Functions”. Constructive Mathematical Analysis 4/1 (Mart 2021), 119-134. https://doi.org/10.33205/cma.863145.
JAMA Campıtı M. On the Korovkin-type approximation of set-valued continuous functions. CMA. 2021;4:119–134.
MLA Campıtı, Michele. “On the Korovkin-Type Approximation of Set-Valued Continuous Functions”. Constructive Mathematical Analysis, c. 4, sy. 1, 2021, ss. 119-34, doi:10.33205/cma.863145.
Vancouver Campıtı M. On the Korovkin-type approximation of set-valued continuous functions. CMA. 2021;4(1):119-34.

Cited By

Local Korovkin-type approximation problems for bounded function spaces
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https://doi.org/10.1007/s13398-024-01589-w