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Bivariate Cheney-Sharma operators on simplex

Yıl 2018, Cilt: 47 Sayı: 4, 793 - 804, 01.08.2018

Öz

In this paper, we consider bivariate Cheney-Sharma operators which are not the tensor product construction. Precisely, we show that these operators preserve Lipschitz condition of a given Lipschitz continuous function $f$ and also the properties of the modulus of continuity function
when $f$ is a modulus of continuity function.

Kaynakça

  • Agratini, O. and Rus, I. A. Iterates of a class of dicsrete linear operators via contraction principle, Comment. Math. Univ. Carolin. 44(3), 555-563, 2003.
  • Altomare, F. and Campiti, M. Korovkin-type approximaton theory and its applications, (Walter de Gruyter, Berlin-New York, 1994).
  • Başcanbaz-Tunca, G. and Tuncer, Y. On a Chlodovsky variant of a multivariate beta operator, J. Comput. Appl. Math. 235(16), 4816-4824, 2011.
  • Başcanbaz-Tunca, G. and Taşdelen, F. On Chlodovsky form of the Meyer-König and Zeller operators, An. Univ. Vest Timiş. Ser. Mat.- Inform. 49(2), 137-144, 2011.
  • Başcanbaz-Tunca, G., ݝnce-ݝlarslan, H. G. and Erençin, A. Bivariate Bernstein type operators, Appl. Math. Comput. 273, 543-552, 2016.
  • Başcanbaz-Tunca, G., Erençin, A. and Taşdelen, F. Some properties of Bernstein type Cheney and Sharma operators(accepted).
  • Brown, B.M., Elliott, D. and Paget, D.F. Lipschitz constants for the Bernstein polynomials of a Lipschitz continuous function, J. Approx. Theory 49(2), 196-199, 1987.
  • Cao, F. Modulus of continuity, K-functional and Stancu operator on a simplex, Indian J. Pure Appl. Math. 35(12), 1343-1364, 2004.
  • Cao, F., Ding, C. and Xu, Z. On multivariate Baskakov operator, J. Math. Anal. Appl. 307(1), 274-291, 2005.
  • Catinaş, T. and Otrocol, D. Iterates of multivariate Cheney-Sharma operators, J. Comput. Anal. Appl. 15(7), 1240-1246, 2013.
  • Cheney, E. W. and Sharma, A. On a generalization of Bernstein polynomials, Riv. Mat. Univ. Parma 2(5), 77-84, 1964.
  • Craciun, M. Approximation operators constructed by means of Sheer sequences, Rev. Anal. Numér. Théor. Approx. 30(2), 135-150, 2001.
  • Ding, C. and Cao, F. K-functionals and multivariate Bernstein polynomials, J. Approx. Theory, 155(2), 125-135, 2008.
  • Erençin, A., Başcanbaz-Tunca, G. and Taşdelen, F. Some preservation properties of MKZ-Stancu type operators, Sarajevo J. Math., 10(22)(1), 93-102, 2014.
  • Erençin, A., Başcanbaz-Tunca, G. and Taşdelen, F. Some properties of the operators defined by Lupaş, Rev. Anal. Numér. Théor. Approx. 43(2), 168-174, 2014.
  • Farcaş, M. D. About Bernstein polynomials, An. Univ. Craiova Ser. Mat. Inform. 35, 117- 121, 2008.
  • Khan, M. K. Approximation properties of Beta operators, Progress in approximation theory, (Academic Press, Boston, MA, 1991), 483-495.
  • Khan, M. K. and Peters, M. A. Lipschitz constants for some approximation operators of a Lipschitz continuous function, J. Approx. Theory 59(3), 307-315, 1989.
  • Li, Z. Bernstein polynomials and modulus of continuity, J. Approx. Theory 102(1), 171-174, 2000.
  • Lindvall, T. Bernstein polynomials and the law of large numbers, Math. Sci. 7(2), 127-139, 1982.
  • Stancu, D. D. and Cismaşiu, C. On an approximating linear positive operator of Cheney- Sharma, Rev. Anal. Numér. Théor. Approx. 26(1-2), 221-227, 1997.
  • Stancu, D. D., Cabulea, L. A. and Pop, D. Approximation of bivariate functions by means of the operators $S_{m,n}^{\alpha,\beta;a,b}$, Stud. Univ. Babeş-Bolyai Math. 47(4), 105-113, 2002.
  • Stancu, D. D. Use of an identity of A. Hurwitz for construction of a linear positive operator of approximation, Rev. Anal. Numér. Théor. Approx. 31(1), 115-118, 2002.
  • Stancu, D. D. and Stoica, E. I. On the use Abel-Jensen type combinatorial formulas for construction and investigation of some algebraic polynomial operators of approximation, Stud. Univ. Babeş-Bolyai Math. 54(4), 167-182, 2009.
  • Stoica, E. I. On the combinatorial identities of Abel-Hurwitz type and their use in constructive theory of functions , Stud. Univ. Babeş-Bolyai Math. 55(4), 249-257, 2010.
  • Taşcu, I. Approximation of bivariate functions by operators of Stancu-Hurwitz type, Facta Univ. Ser. Math. Inform. 20, 33-39, 2005.
  • Taşcu, I. and Horvat-Marc, A. Construction of Stancu-Hurwitz operator for two variables, Acta Univ. Apulensis Math. Inform. 11, 97-101, 2006.
  • Trif, T. An elementary proof of the preservation of Lipschitz constants by the Meyer-König and Zeller operators, J. Inequal. Pure Appl. Math. 4(5), Article90, 3pp., 2003.
Yıl 2018, Cilt: 47 Sayı: 4, 793 - 804, 01.08.2018

Öz

Kaynakça

  • Agratini, O. and Rus, I. A. Iterates of a class of dicsrete linear operators via contraction principle, Comment. Math. Univ. Carolin. 44(3), 555-563, 2003.
  • Altomare, F. and Campiti, M. Korovkin-type approximaton theory and its applications, (Walter de Gruyter, Berlin-New York, 1994).
  • Başcanbaz-Tunca, G. and Tuncer, Y. On a Chlodovsky variant of a multivariate beta operator, J. Comput. Appl. Math. 235(16), 4816-4824, 2011.
  • Başcanbaz-Tunca, G. and Taşdelen, F. On Chlodovsky form of the Meyer-König and Zeller operators, An. Univ. Vest Timiş. Ser. Mat.- Inform. 49(2), 137-144, 2011.
  • Başcanbaz-Tunca, G., ݝnce-ݝlarslan, H. G. and Erençin, A. Bivariate Bernstein type operators, Appl. Math. Comput. 273, 543-552, 2016.
  • Başcanbaz-Tunca, G., Erençin, A. and Taşdelen, F. Some properties of Bernstein type Cheney and Sharma operators(accepted).
  • Brown, B.M., Elliott, D. and Paget, D.F. Lipschitz constants for the Bernstein polynomials of a Lipschitz continuous function, J. Approx. Theory 49(2), 196-199, 1987.
  • Cao, F. Modulus of continuity, K-functional and Stancu operator on a simplex, Indian J. Pure Appl. Math. 35(12), 1343-1364, 2004.
  • Cao, F., Ding, C. and Xu, Z. On multivariate Baskakov operator, J. Math. Anal. Appl. 307(1), 274-291, 2005.
  • Catinaş, T. and Otrocol, D. Iterates of multivariate Cheney-Sharma operators, J. Comput. Anal. Appl. 15(7), 1240-1246, 2013.
  • Cheney, E. W. and Sharma, A. On a generalization of Bernstein polynomials, Riv. Mat. Univ. Parma 2(5), 77-84, 1964.
  • Craciun, M. Approximation operators constructed by means of Sheer sequences, Rev. Anal. Numér. Théor. Approx. 30(2), 135-150, 2001.
  • Ding, C. and Cao, F. K-functionals and multivariate Bernstein polynomials, J. Approx. Theory, 155(2), 125-135, 2008.
  • Erençin, A., Başcanbaz-Tunca, G. and Taşdelen, F. Some preservation properties of MKZ-Stancu type operators, Sarajevo J. Math., 10(22)(1), 93-102, 2014.
  • Erençin, A., Başcanbaz-Tunca, G. and Taşdelen, F. Some properties of the operators defined by Lupaş, Rev. Anal. Numér. Théor. Approx. 43(2), 168-174, 2014.
  • Farcaş, M. D. About Bernstein polynomials, An. Univ. Craiova Ser. Mat. Inform. 35, 117- 121, 2008.
  • Khan, M. K. Approximation properties of Beta operators, Progress in approximation theory, (Academic Press, Boston, MA, 1991), 483-495.
  • Khan, M. K. and Peters, M. A. Lipschitz constants for some approximation operators of a Lipschitz continuous function, J. Approx. Theory 59(3), 307-315, 1989.
  • Li, Z. Bernstein polynomials and modulus of continuity, J. Approx. Theory 102(1), 171-174, 2000.
  • Lindvall, T. Bernstein polynomials and the law of large numbers, Math. Sci. 7(2), 127-139, 1982.
  • Stancu, D. D. and Cismaşiu, C. On an approximating linear positive operator of Cheney- Sharma, Rev. Anal. Numér. Théor. Approx. 26(1-2), 221-227, 1997.
  • Stancu, D. D., Cabulea, L. A. and Pop, D. Approximation of bivariate functions by means of the operators $S_{m,n}^{\alpha,\beta;a,b}$, Stud. Univ. Babeş-Bolyai Math. 47(4), 105-113, 2002.
  • Stancu, D. D. Use of an identity of A. Hurwitz for construction of a linear positive operator of approximation, Rev. Anal. Numér. Théor. Approx. 31(1), 115-118, 2002.
  • Stancu, D. D. and Stoica, E. I. On the use Abel-Jensen type combinatorial formulas for construction and investigation of some algebraic polynomial operators of approximation, Stud. Univ. Babeş-Bolyai Math. 54(4), 167-182, 2009.
  • Stoica, E. I. On the combinatorial identities of Abel-Hurwitz type and their use in constructive theory of functions , Stud. Univ. Babeş-Bolyai Math. 55(4), 249-257, 2010.
  • Taşcu, I. Approximation of bivariate functions by operators of Stancu-Hurwitz type, Facta Univ. Ser. Math. Inform. 20, 33-39, 2005.
  • Taşcu, I. and Horvat-Marc, A. Construction of Stancu-Hurwitz operator for two variables, Acta Univ. Apulensis Math. Inform. 11, 97-101, 2006.
  • Trif, T. An elementary proof of the preservation of Lipschitz constants by the Meyer-König and Zeller operators, J. Inequal. Pure Appl. Math. 4(5), Article90, 3pp., 2003.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Gülen Başcanbaz-tunca

Ayşegül Erençin

Hatice Gül İnce-ilarslan

Yayımlanma Tarihi 1 Ağustos 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 47 Sayı: 4

Kaynak Göster

APA Başcanbaz-tunca, G., Erençin, A., & İnce-ilarslan, H. G. (2018). Bivariate Cheney-Sharma operators on simplex. Hacettepe Journal of Mathematics and Statistics, 47(4), 793-804.
AMA Başcanbaz-tunca G, Erençin A, İnce-ilarslan HG. Bivariate Cheney-Sharma operators on simplex. Hacettepe Journal of Mathematics and Statistics. Ağustos 2018;47(4):793-804.
Chicago Başcanbaz-tunca, Gülen, Ayşegül Erençin, ve Hatice Gül İnce-ilarslan. “Bivariate Cheney-Sharma Operators on Simplex”. Hacettepe Journal of Mathematics and Statistics 47, sy. 4 (Ağustos 2018): 793-804.
EndNote Başcanbaz-tunca G, Erençin A, İnce-ilarslan HG (01 Ağustos 2018) Bivariate Cheney-Sharma operators on simplex. Hacettepe Journal of Mathematics and Statistics 47 4 793–804.
IEEE G. Başcanbaz-tunca, A. Erençin, ve H. G. İnce-ilarslan, “Bivariate Cheney-Sharma operators on simplex”, Hacettepe Journal of Mathematics and Statistics, c. 47, sy. 4, ss. 793–804, 2018.
ISNAD Başcanbaz-tunca, Gülen vd. “Bivariate Cheney-Sharma Operators on Simplex”. Hacettepe Journal of Mathematics and Statistics 47/4 (Ağustos 2018), 793-804.
JAMA Başcanbaz-tunca G, Erençin A, İnce-ilarslan HG. Bivariate Cheney-Sharma operators on simplex. Hacettepe Journal of Mathematics and Statistics. 2018;47:793–804.
MLA Başcanbaz-tunca, Gülen vd. “Bivariate Cheney-Sharma Operators on Simplex”. Hacettepe Journal of Mathematics and Statistics, c. 47, sy. 4, 2018, ss. 793-04.
Vancouver Başcanbaz-tunca G, Erençin A, İnce-ilarslan HG. Bivariate Cheney-Sharma operators on simplex. Hacettepe Journal of Mathematics and Statistics. 2018;47(4):793-804.