BibTex RIS Kaynak Göster

Approximation Properties of Stancu Type Meyer-König andZeller Operators

Yıl 2013, Cilt: 42 Sayı: 2, 139 - 148, 01.02.2013

Öz

In this paper, we introduce a Stancu type modification of the q- MeyerK¨ onig and Zeller operators and investigate the Korovkin type statisticalapproximation properties of this modification via A−statistical convergence. We also compute rate of convergence of the defined operatorsby means of modulus of continuity. Furthermore, we give an rth order generalization of our operators and obtain approximation results ofthem.

Kaynakça

  • Agratini O., On a q−analogue of Stancu operators, Cent Eur J Math, 8(1), 191-198, 2010. Agratini O., Statistical convergence of a non-positive approximation process, Chaos Solitons Fractals, 44, 977-981, 2011.
  • Altomare F, Campiti M., Korovkin-type approximation theory and its applications, Walter de Gruyter studies in math. Berlin:de Gruyter&Co, 1994.
  • Andrews GE, Askey R. Roy R., Special functions, Cambridge University Press, 1999.
  • Cheney EW, Sharma A., Bernstein power series, Can J Math, 16, 241-243, 1964.
  • Do˘ gru O., Duman O., Statistical approximation of Meyer-K¨ onig and Zeller operators based on the q−integers, Publ Math Debrecen, 68, 199-214, 2006.
  • Duman O, Orhan C., An abstract version of the Korovkin approximation theorem. Publ Math Debrecen 69, 33-46, 2006.
  • Fast H. Sur la convergence statistique. Collog Math, 2, 241-244, 1951.
  • Fridy JA. On statistical convergence. Analysis, 5, 301-313, 1985.
  • Gadjiev AD, Orhan C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math, 32, 129-138, 2002.
  • Hardy GH., Divergent series, (Oxford Univ. Press) London, 1949.
  • Kolk E., Matrix summability of statistically convergent sequences, Analysis, 13, 77-83, 1993. Korovkin PP., Linear operators and the theory of approximation, India, Delhi: Hindustan Publishing Corp, 1960.
  • Kirov G, Popova L., A generalization of the linear positive operators, Math. Balkanica NS, 7, 149-162, 1993.
  • Lupa¸ s A., A q−analoque of the Bernstein operator. University of Cluj-Napoca Seminar on Numerical and Statistical Calculus Preprint, 9, 85-92, 1987.
  • Lupa¸ s A., A q−analoques of Stancu operators, Math. Anal. Approx. Theor. The 5th Romanian-German Seminar on Approximation Theory and its Application, 145-154, 2002. Meyer-K¨ onig W, Zeller K., Bernsteinsche potenzreihen, Studia Math., 19, 89-94, 1960.
  • Nowak G., Approximation properties for generalized q−Bernstein polynomials, J Math Anal Appl, 350, 50-55, 2009.
  • ¨ Ozarslan MA, Duman O. Approximation theorems by Meyer-K¨ onig and Zeller type operators. Chaos Solitons Fractals 41, 451-456, 2009.
  • Phillips GM., Bernstein polynomials based on the q−integers, Ann Numer Math 4, 511-518, 19 Stancu DD. Approximation of functions by a new class of linear polynomial operators. Rev Roumaine Math Pures Appl 8, 1173-1194, 1968.
  • Trif T., Meyer-K¨ onig and Zeller operators based on the q−integers, Rev Anal Num´ er Th´ eor Approx. 29, 221-229, 2000.
  • Verma DK, Gupta V, Agrawal PN., Some approximation properties of Baskakov-DurrmeyerStancu operators, Appl. Math. Comput., 218(11), 6549–6556, 2012.

Approximation Properties of Stancu Type Meyer-König andZeller Operators

Yıl 2013, Cilt: 42 Sayı: 2, 139 - 148, 01.02.2013

Öz

-

Kaynakça

  • Agratini O., On a q−analogue of Stancu operators, Cent Eur J Math, 8(1), 191-198, 2010. Agratini O., Statistical convergence of a non-positive approximation process, Chaos Solitons Fractals, 44, 977-981, 2011.
  • Altomare F, Campiti M., Korovkin-type approximation theory and its applications, Walter de Gruyter studies in math. Berlin:de Gruyter&Co, 1994.
  • Andrews GE, Askey R. Roy R., Special functions, Cambridge University Press, 1999.
  • Cheney EW, Sharma A., Bernstein power series, Can J Math, 16, 241-243, 1964.
  • Do˘ gru O., Duman O., Statistical approximation of Meyer-K¨ onig and Zeller operators based on the q−integers, Publ Math Debrecen, 68, 199-214, 2006.
  • Duman O, Orhan C., An abstract version of the Korovkin approximation theorem. Publ Math Debrecen 69, 33-46, 2006.
  • Fast H. Sur la convergence statistique. Collog Math, 2, 241-244, 1951.
  • Fridy JA. On statistical convergence. Analysis, 5, 301-313, 1985.
  • Gadjiev AD, Orhan C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math, 32, 129-138, 2002.
  • Hardy GH., Divergent series, (Oxford Univ. Press) London, 1949.
  • Kolk E., Matrix summability of statistically convergent sequences, Analysis, 13, 77-83, 1993. Korovkin PP., Linear operators and the theory of approximation, India, Delhi: Hindustan Publishing Corp, 1960.
  • Kirov G, Popova L., A generalization of the linear positive operators, Math. Balkanica NS, 7, 149-162, 1993.
  • Lupa¸ s A., A q−analoque of the Bernstein operator. University of Cluj-Napoca Seminar on Numerical and Statistical Calculus Preprint, 9, 85-92, 1987.
  • Lupa¸ s A., A q−analoques of Stancu operators, Math. Anal. Approx. Theor. The 5th Romanian-German Seminar on Approximation Theory and its Application, 145-154, 2002. Meyer-K¨ onig W, Zeller K., Bernsteinsche potenzreihen, Studia Math., 19, 89-94, 1960.
  • Nowak G., Approximation properties for generalized q−Bernstein polynomials, J Math Anal Appl, 350, 50-55, 2009.
  • ¨ Ozarslan MA, Duman O. Approximation theorems by Meyer-K¨ onig and Zeller type operators. Chaos Solitons Fractals 41, 451-456, 2009.
  • Phillips GM., Bernstein polynomials based on the q−integers, Ann Numer Math 4, 511-518, 19 Stancu DD. Approximation of functions by a new class of linear polynomial operators. Rev Roumaine Math Pures Appl 8, 1173-1194, 1968.
  • Trif T., Meyer-K¨ onig and Zeller operators based on the q−integers, Rev Anal Num´ er Th´ eor Approx. 29, 221-229, 2000.
  • Verma DK, Gupta V, Agrawal PN., Some approximation properties of Baskakov-DurrmeyerStancu operators, Appl. Math. Comput., 218(11), 6549–6556, 2012.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Matematik
Yazarlar

Mediha Örkçü Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 42 Sayı: 2

Kaynak Göster

APA Örkçü, M. (2013). Approximation Properties of Stancu Type Meyer-König andZeller Operators. Hacettepe Journal of Mathematics and Statistics, 42(2), 139-148.
AMA Örkçü M. Approximation Properties of Stancu Type Meyer-König andZeller Operators. Hacettepe Journal of Mathematics and Statistics. Şubat 2013;42(2):139-148.
Chicago Örkçü, Mediha. “Approximation Properties of Stancu Type Meyer-König AndZeller Operators”. Hacettepe Journal of Mathematics and Statistics 42, sy. 2 (Şubat 2013): 139-48.
EndNote Örkçü M (01 Şubat 2013) Approximation Properties of Stancu Type Meyer-König andZeller Operators. Hacettepe Journal of Mathematics and Statistics 42 2 139–148.
IEEE M. Örkçü, “Approximation Properties of Stancu Type Meyer-König andZeller Operators”, Hacettepe Journal of Mathematics and Statistics, c. 42, sy. 2, ss. 139–148, 2013.
ISNAD Örkçü, Mediha. “Approximation Properties of Stancu Type Meyer-König AndZeller Operators”. Hacettepe Journal of Mathematics and Statistics 42/2 (Şubat 2013), 139-148.
JAMA Örkçü M. Approximation Properties of Stancu Type Meyer-König andZeller Operators. Hacettepe Journal of Mathematics and Statistics. 2013;42:139–148.
MLA Örkçü, Mediha. “Approximation Properties of Stancu Type Meyer-König AndZeller Operators”. Hacettepe Journal of Mathematics and Statistics, c. 42, sy. 2, 2013, ss. 139-48.
Vancouver Örkçü M. Approximation Properties of Stancu Type Meyer-König andZeller Operators. Hacettepe Journal of Mathematics and Statistics. 2013;42(2):139-48.