Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 68 Sayı: 1, 187 - 196, 01.02.2019
https://doi.org/10.31801/cfsuasmas.443703

Öz

Kaynakça

  • Aral, A., A Generalization of Szász-Mirakyan Operators besed on q-integers, Math.Comp. Modelling, 47(2008), 1052-1062.
  • Becker, M., Global approximation theorems for Szász-Mirakyan and Baskakov in polynomial weighted spaces, Indian Univer. Math. J., 27 (1978), 127-14.
  • Stancu, D. D., A new class of uniform approximating polynomial operators in two and several variables, Prooc. of Conf. on the Constr. Theory of Func. (ApproximationTheory, Budapest,1969), 443-455, 1972.
  • Duman, E. E., Duman, O., Integral-type generalizations of operators obtained from certain multivariate polynomials, Calcolo,Volume 45, Issue 1, pp 53--67(2008).
  • Erençin, A. , Tunca, G.B. and Taşdelen, F., Kantorovich type q-Bernstein-Stancu operators, Stud. Univ. Babe¸ s-Bolyai Math. 57 (2012), No. 1, 89--105.
  • Firlej, B., Lesniewicz, M, Rempulska L., Approximation of Functions Two Variables by Some Operators in Weighted Spaces, Rendiconti del Seminario Matematico della Universita di Padova, Tome 101(1999), p.63-82.
  • Kantorovich, L.V., Sur certain developments suivant les polynomes de la forme de S. Bernstein, I,II, C.R. Acad. URSS(1930), 563-568, 595-600.
  • Gupta P., Gupta V., Rate of Convergence on Baskakov-Szász operators type operators, Fasc. Math., 31(2001), 37-44.
  • Gupta V., Agrawall Ravi P., Convergence Estimates in Approximation Theory, Springer, Switzerland, (2014).
  • Moreno, A.J.L., Delgado, F.J.M., Asymtotic Expansion of Multivariate Kantorovich Type Operators, Numerical Algorithms, (2005), 39, 237-252.
  • Olgun, A., Some Properties of The Multivariate Szazs Operators, Comptes rendus de I'Academie Bulgare des Sciences, Tome 65, No 2 ( 2012),139-146.
  • O. Dogru, Özalp, N., Approximation by Kantorovich type generalization of Meyer-König and Zeller operators, Glasnik Mat. (2001), No 36, 311-317.
  • Özarslan, M.A., Duman, O. and Srivastava, H.M., Statistical Apparoximation Resullts for Kantorovich-Type Operators Involving Some Special Polynomials, Mathematical and Computer Modelling, 48 (3)(2008), 388-401.
  • Özhavzalı, M., On Properties For Some Kantorovich-Type Operators, Lambert Publishing, Germany, (2016).
  • Özhavzalı, M., Olgun, A., Approximation Properties For Modified Kantorovich-Type Operators, Journal of Mathematics and System Science, 5 (2015), 18-26.
  • Rempulska, L., Walczak, Z., Modified Szász-Mirakyan Operators, Mathematica Balkanica, New Series, vol. 18,(2001), Fasc. 1-2.
  • Taşdelen, F., Aktaş, R. and Altın, A., Kantorovich Type of Szasz Operators Including Brenke-Type Polynomials, Abstract and Applied Analysis, (2012), doi:10.1155/2012/867203.
  • Tasdelen F., Olgun A., Tunca, G. B., Approximation of functions of two variables by certain linear positive operators, Proc. Indian Acad. Sci.,(2005), Vol.117 No.3, 387--399.
  • Totic, V., Approximation by Szász-Mirakyan-Kantorovich Operators in L^{p}(p>1), Analysis Math, 9 (1983)147--167.
  • Walczak, Z., Approximation of Functions of Two Variables by Some Linear Positive Operators, Acta Math. Univ. Comenianae, vol. LXXIV,1 (2005), pp.37--48.
  • Walczak, Z., On Certain Positive Linear Operators in Polinomial Weight Spaces, Acta Math. Hungar., 101(3) (2003), pp.179-191.

On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators

Yıl 2019, Cilt: 68 Sayı: 1, 187 - 196, 01.02.2019
https://doi.org/10.31801/cfsuasmas.443703

Öz

In the present paper, we introduce certain modification of Szász-Mirakyan-Kantorovich-type operators in polynomial weighted spaces of continuous functions of two variables. Then we research some approximation properties of these operators. We give some inequalities for the operators by means of the weighted modulus of continuity and also obtain a Voronovskaya-type theorem. Furthermore, in the paper we show that our operators give better degree of approximation of functions belonging to weighted spaces than classical Szász-Mirakyan operators.

Kaynakça

  • Aral, A., A Generalization of Szász-Mirakyan Operators besed on q-integers, Math.Comp. Modelling, 47(2008), 1052-1062.
  • Becker, M., Global approximation theorems for Szász-Mirakyan and Baskakov in polynomial weighted spaces, Indian Univer. Math. J., 27 (1978), 127-14.
  • Stancu, D. D., A new class of uniform approximating polynomial operators in two and several variables, Prooc. of Conf. on the Constr. Theory of Func. (ApproximationTheory, Budapest,1969), 443-455, 1972.
  • Duman, E. E., Duman, O., Integral-type generalizations of operators obtained from certain multivariate polynomials, Calcolo,Volume 45, Issue 1, pp 53--67(2008).
  • Erençin, A. , Tunca, G.B. and Taşdelen, F., Kantorovich type q-Bernstein-Stancu operators, Stud. Univ. Babe¸ s-Bolyai Math. 57 (2012), No. 1, 89--105.
  • Firlej, B., Lesniewicz, M, Rempulska L., Approximation of Functions Two Variables by Some Operators in Weighted Spaces, Rendiconti del Seminario Matematico della Universita di Padova, Tome 101(1999), p.63-82.
  • Kantorovich, L.V., Sur certain developments suivant les polynomes de la forme de S. Bernstein, I,II, C.R. Acad. URSS(1930), 563-568, 595-600.
  • Gupta P., Gupta V., Rate of Convergence on Baskakov-Szász operators type operators, Fasc. Math., 31(2001), 37-44.
  • Gupta V., Agrawall Ravi P., Convergence Estimates in Approximation Theory, Springer, Switzerland, (2014).
  • Moreno, A.J.L., Delgado, F.J.M., Asymtotic Expansion of Multivariate Kantorovich Type Operators, Numerical Algorithms, (2005), 39, 237-252.
  • Olgun, A., Some Properties of The Multivariate Szazs Operators, Comptes rendus de I'Academie Bulgare des Sciences, Tome 65, No 2 ( 2012),139-146.
  • O. Dogru, Özalp, N., Approximation by Kantorovich type generalization of Meyer-König and Zeller operators, Glasnik Mat. (2001), No 36, 311-317.
  • Özarslan, M.A., Duman, O. and Srivastava, H.M., Statistical Apparoximation Resullts for Kantorovich-Type Operators Involving Some Special Polynomials, Mathematical and Computer Modelling, 48 (3)(2008), 388-401.
  • Özhavzalı, M., On Properties For Some Kantorovich-Type Operators, Lambert Publishing, Germany, (2016).
  • Özhavzalı, M., Olgun, A., Approximation Properties For Modified Kantorovich-Type Operators, Journal of Mathematics and System Science, 5 (2015), 18-26.
  • Rempulska, L., Walczak, Z., Modified Szász-Mirakyan Operators, Mathematica Balkanica, New Series, vol. 18,(2001), Fasc. 1-2.
  • Taşdelen, F., Aktaş, R. and Altın, A., Kantorovich Type of Szasz Operators Including Brenke-Type Polynomials, Abstract and Applied Analysis, (2012), doi:10.1155/2012/867203.
  • Tasdelen F., Olgun A., Tunca, G. B., Approximation of functions of two variables by certain linear positive operators, Proc. Indian Acad. Sci.,(2005), Vol.117 No.3, 387--399.
  • Totic, V., Approximation by Szász-Mirakyan-Kantorovich Operators in L^{p}(p>1), Analysis Math, 9 (1983)147--167.
  • Walczak, Z., Approximation of Functions of Two Variables by Some Linear Positive Operators, Acta Math. Univ. Comenianae, vol. LXXIV,1 (2005), pp.37--48.
  • Walczak, Z., On Certain Positive Linear Operators in Polinomial Weight Spaces, Acta Math. Hungar., 101(3) (2003), pp.179-191.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Müzeyyen Özhavzalı

Ali Olgun Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2019
Gönderilme Tarihi 13 Eylül 2017
Kabul Tarihi 20 Kasım 2017
Yayımlandığı Sayı Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

APA Özhavzalı, M., & Olgun, A. (2019). On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 187-196. https://doi.org/10.31801/cfsuasmas.443703
AMA Özhavzalı M, Olgun A. On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2019;68(1):187-196. doi:10.31801/cfsuasmas.443703
Chicago Özhavzalı, Müzeyyen, ve Ali Olgun. “On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 187-96. https://doi.org/10.31801/cfsuasmas.443703.
EndNote Özhavzalı M, Olgun A (01 Şubat 2019) On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 187–196.
IEEE M. Özhavzalı ve A. Olgun, “On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 187–196, 2019, doi: 10.31801/cfsuasmas.443703.
ISNAD Özhavzalı, Müzeyyen - Olgun, Ali. “On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (Şubat 2019), 187-196. https://doi.org/10.31801/cfsuasmas.443703.
JAMA Özhavzalı M, Olgun A. On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:187–196.
MLA Özhavzalı, Müzeyyen ve Ali Olgun. “On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 187-96, doi:10.31801/cfsuasmas.443703.
Vancouver Özhavzalı M, Olgun A. On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):187-96.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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