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AN UPPER ESTIMATE OF COMPLEX Q-BALÁZS-SZABADOS-KANTOROVICH OPERATORS ON COMPACT DISKS

Year 2016, Volume: 29 Issue: 2, 479 - 486, 21.06.2016

Abstract

In this paper, the complex q-Balázs-Szabados-Kantorovich operators are defined, and a convergence result and an upper quantitative estimate of these operators are given.

 

References

  • Andrews, G.E., Askey, R., Roy, R., Special Functions, Cambridge University Press, Cambridge, (1999).
  • Aral, A, Gupta, V and Agarwal, R.P., Applications of q Calculus in Operator Theory, Springer, Berlin, (2013).
  • Balázs, K., “Approximation by Bernstein type rational function”, Acta Math. Acad. Sci. Hung., 26: 123-134, (1975).
  • Balázs, K., Szabados, J., “Approximation by Bernstein type rational function II”, Acta Math. Acad. Sci. Hung., 40(3-4): 331-337, (1982).
  • Borwein, P., Erdélyi, T., “Sharp extensions of Bernstein's inequality to rational spaces”, Mathematika, 43(2): 412-423, (1996).
  • Dogru, O., “On statistical approximation properties of Stancu type bivariate generalization of q-Balázs –Szabados operators”, In: Proceedings Int. Conf. on Numerical Analysis and Approximation Theory, Casa Cartii de Stiinta Cluj-Napoca, 179-194, (2006).
  • Edward, J.C., Jafari, F., “A complex Rolle's theorem”, Am. Math. Mon., 99(9): 858-861, (1992).
  • Gal, S.G., Approximation by Complex Bernstein and Convolution Type Operators, World Scientific, Hackensack, (2009).
  • Ispir, N., Yildiz Ozkan, E., “Approximation properties of complex q- Balázs-Szabados operators in compact disks”, J. Inequal. Appl., 2013(361), (2013).
  • Kac, V., Cheung, P., Quantum Calculus, Springer, New York, (2002).
  • Kohr, G., Mocanu, P.T., Special Chapters of Complex Analysis, Cluj University Press, Cluj-Napoca, (2005).
  • Korovkin, P.P., Linear operators and the theory of approximation, India, Delhi: Hindustan Publishing Corp., (1960).
  • Yildiz Ozkan, E., “Approximation properties of bivariate complex q- Balázs-Szabados operators of tensor product kind”, J. Inequal. Appl., 2014:20, (2014).
  • Yildiz Ozkan, E., “Approximation by complex bivariate Balázs -Szabados operators”, Bull. Malays. Math. Soc., 39: 1-16, (2016).

An Upper Estimate of Complex q-Balázs-Szabados- Kantorovich Operators on Compact Disks

Year 2016, Volume: 29 Issue: 2, 479 - 486, 21.06.2016

Abstract

References

  • Andrews, G.E., Askey, R., Roy, R., Special Functions, Cambridge University Press, Cambridge, (1999).
  • Aral, A, Gupta, V and Agarwal, R.P., Applications of q Calculus in Operator Theory, Springer, Berlin, (2013).
  • Balázs, K., “Approximation by Bernstein type rational function”, Acta Math. Acad. Sci. Hung., 26: 123-134, (1975).
  • Balázs, K., Szabados, J., “Approximation by Bernstein type rational function II”, Acta Math. Acad. Sci. Hung., 40(3-4): 331-337, (1982).
  • Borwein, P., Erdélyi, T., “Sharp extensions of Bernstein's inequality to rational spaces”, Mathematika, 43(2): 412-423, (1996).
  • Dogru, O., “On statistical approximation properties of Stancu type bivariate generalization of q-Balázs –Szabados operators”, In: Proceedings Int. Conf. on Numerical Analysis and Approximation Theory, Casa Cartii de Stiinta Cluj-Napoca, 179-194, (2006).
  • Edward, J.C., Jafari, F., “A complex Rolle's theorem”, Am. Math. Mon., 99(9): 858-861, (1992).
  • Gal, S.G., Approximation by Complex Bernstein and Convolution Type Operators, World Scientific, Hackensack, (2009).
  • Ispir, N., Yildiz Ozkan, E., “Approximation properties of complex q- Balázs-Szabados operators in compact disks”, J. Inequal. Appl., 2013(361), (2013).
  • Kac, V., Cheung, P., Quantum Calculus, Springer, New York, (2002).
  • Kohr, G., Mocanu, P.T., Special Chapters of Complex Analysis, Cluj University Press, Cluj-Napoca, (2005).
  • Korovkin, P.P., Linear operators and the theory of approximation, India, Delhi: Hindustan Publishing Corp., (1960).
  • Yildiz Ozkan, E., “Approximation properties of bivariate complex q- Balázs-Szabados operators of tensor product kind”, J. Inequal. Appl., 2014:20, (2014).
  • Yildiz Ozkan, E., “Approximation by complex bivariate Balázs -Szabados operators”, Bull. Malays. Math. Soc., 39: 1-16, (2016).
There are 14 citations in total.

Details

Journal Section Mathematics
Authors

Esma Yıldız Özkan

Publication Date June 21, 2016
Published in Issue Year 2016 Volume: 29 Issue: 2

Cite

APA Yıldız Özkan, E. (2016). AN UPPER ESTIMATE OF COMPLEX Q-BALÁZS-SZABADOS-KANTOROVICH OPERATORS ON COMPACT DISKS. Gazi University Journal of Science, 29(2), 479-486.
AMA Yıldız Özkan E. AN UPPER ESTIMATE OF COMPLEX Q-BALÁZS-SZABADOS-KANTOROVICH OPERATORS ON COMPACT DISKS. Gazi University Journal of Science. June 2016;29(2):479-486.
Chicago Yıldız Özkan, Esma. “AN UPPER ESTIMATE OF COMPLEX Q-BALÁZS-SZABADOS-KANTOROVICH OPERATORS ON COMPACT DISKS”. Gazi University Journal of Science 29, no. 2 (June 2016): 479-86.
EndNote Yıldız Özkan E (June 1, 2016) AN UPPER ESTIMATE OF COMPLEX Q-BALÁZS-SZABADOS-KANTOROVICH OPERATORS ON COMPACT DISKS. Gazi University Journal of Science 29 2 479–486.
IEEE E. Yıldız Özkan, “AN UPPER ESTIMATE OF COMPLEX Q-BALÁZS-SZABADOS-KANTOROVICH OPERATORS ON COMPACT DISKS”, Gazi University Journal of Science, vol. 29, no. 2, pp. 479–486, 2016.
ISNAD Yıldız Özkan, Esma. “AN UPPER ESTIMATE OF COMPLEX Q-BALÁZS-SZABADOS-KANTOROVICH OPERATORS ON COMPACT DISKS”. Gazi University Journal of Science 29/2 (June 2016), 479-486.
JAMA Yıldız Özkan E. AN UPPER ESTIMATE OF COMPLEX Q-BALÁZS-SZABADOS-KANTOROVICH OPERATORS ON COMPACT DISKS. Gazi University Journal of Science. 2016;29:479–486.
MLA Yıldız Özkan, Esma. “AN UPPER ESTIMATE OF COMPLEX Q-BALÁZS-SZABADOS-KANTOROVICH OPERATORS ON COMPACT DISKS”. Gazi University Journal of Science, vol. 29, no. 2, 2016, pp. 479-86.
Vancouver Yıldız Özkan E. AN UPPER ESTIMATE OF COMPLEX Q-BALÁZS-SZABADOS-KANTOROVICH OPERATORS ON COMPACT DISKS. Gazi University Journal of Science. 2016;29(2):479-86.