Research Article
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Year 2019, Volume: 68 Issue: 1, 187 - 196, 01.02.2019

Müzeyyen Özhavzalı Ali Olgun

https://doi.org/10.31801/cfsuasmas.443703

Abstract

References

  • 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

Year 2019, Volume: 68 Issue: 1, 187 - 196, 01.02.2019

Müzeyyen Özhavzalı Ali Olgun

https://doi.org/10.31801/cfsuasmas.443703

Abstract

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.

Keywords

Kantorovich-type operators modulus of continuity weighted spaces Voronovskaya-type theorem

References

  • 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.
There are 21 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Müzeyyen Özhavzalı

Ali Olgun This is me

Publication Date February 1, 2019
Submission Date September 13, 2017
Acceptance Date November 20, 2017
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

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. February 2019;68(1):187-196. doi:10.31801/cfsuasmas.443703
Chicago Özhavzalı, Müzeyyen, and 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, no. 1 (February 2019): 187-96. https://doi.org/10.31801/cfsuasmas.443703.
EndNote Özhavzalı M, Olgun A (February 1, 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 and A. Olgun, “On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 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 (February 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 and 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, vol. 68, no. 1, 2019, pp. 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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