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Year 2020, Volume: 49 Issue: 3, 1030 - 1038, 02.06.2020
https://doi.org/10.15672/hujms.549015

Abstract

References

  • [1] T. Acar, A.M. Acu and N. Manav, Approximation of functions by genuine Bernstein- Durrmeyer type operators, J. Math. Ineq. 12 (4), 975–987, 2018.
  • [2] F. Altomare and M. Campiti, Korovkin-type Approximation Theory and its Applica- tions, de Gruyter Series Studies in Mathematics, Vol. 17, Walter de Gruyter & Co., Berlin, New York, 1994.
  • [3] I. Chlodovsky, Sur le développement des fonctions définies dans un interval infini en séries de polynômes de N.S. Bernstein, Compositio Math. 4, 380–393, 1937.
  • [4] A.D. Gadjiev, Theorems of Korovkin type, Mat. Zametki, 20 (5), 781–786 (in Rus- sian), 1976; Mathematical Notes, 20 (5), 995-998 (English translation), 1976.
  • [5] A.D. Gadjiev and A. Aral, The estimates of approximation by using a new type of weighted modulus of continuity, Comput. Math. Appl. 54, 127–135, 2007.
  • [6] A.D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32, 129–138, 2002.
  • [7] V. Gupta and M.A. Noor, Convergence of derivatives for certain mixed Szász-Beta operators, J. Math. Anal. Appl. 321, 1–9, 2006.
  • [8] G.C. Jain, Approximation of functions by a new class of linear operators, J. Aust. Math. Soc. 13 (3), 271–276, 1972.
  • [9] A.S. Kumar and T. Acar, Approximation by generalized Baskakov-Durrmeyer-Stancu type operators, Rend. Circ. Mat. Palermo, Series 2, 65 (3), 411–424, 2016.
  • [10] G.G. Lorentz, Approximation of functions, Holt, Rinehart and Winston, Inc., New York, 1966.
  • [11] G.G. Lorentz, Bernstein Polynomials, 2nd Ed., Chelsea Publ. Comp., New York, NY, 1986.
  • [12] G. Mastroianni, Su un operatore lineare e positivo, Rend. Acc. Sc. Fis. Mat. Napoli, 46, 161,-176, 1979.
  • [13] C.A. Micchelli, Saturation classes and iterates of operators, Dissertation, Stanford, 1969.
  • [14] M. Mursaleen and M. Nasiruzzaman, Approximation of modified Jakimovski-Leviatan- Beta type operators, Constr. Math. Anal. 1 (2), 88–98, 2018.
  • [15] P.C. Sikkema, On some linear positive operators, Indag. Math. 32, 327–337, 1970.
  • [16] S. Tarabie, On Jain-Beta linear operators, Appl. Math. Inform. Sci. 6 (2), 213–216, 2012.

Linear positive operators constructed by using Beta-type bases

Year 2020, Volume: 49 Issue: 3, 1030 - 1038, 02.06.2020
https://doi.org/10.15672/hujms.549015

Abstract

Starting from a discrete linear approximation process that has the ability to turn polynomials into polynomials of the same degree, we introduce an integral generalization by using Beta-type bases. Some properties of this new sequence of operators are investigated in unweighted and weighted spaces of functions defined on unbounded interval. In our construction particular cases are outlined.

References

  • [1] T. Acar, A.M. Acu and N. Manav, Approximation of functions by genuine Bernstein- Durrmeyer type operators, J. Math. Ineq. 12 (4), 975–987, 2018.
  • [2] F. Altomare and M. Campiti, Korovkin-type Approximation Theory and its Applica- tions, de Gruyter Series Studies in Mathematics, Vol. 17, Walter de Gruyter & Co., Berlin, New York, 1994.
  • [3] I. Chlodovsky, Sur le développement des fonctions définies dans un interval infini en séries de polynômes de N.S. Bernstein, Compositio Math. 4, 380–393, 1937.
  • [4] A.D. Gadjiev, Theorems of Korovkin type, Mat. Zametki, 20 (5), 781–786 (in Rus- sian), 1976; Mathematical Notes, 20 (5), 995-998 (English translation), 1976.
  • [5] A.D. Gadjiev and A. Aral, The estimates of approximation by using a new type of weighted modulus of continuity, Comput. Math. Appl. 54, 127–135, 2007.
  • [6] A.D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32, 129–138, 2002.
  • [7] V. Gupta and M.A. Noor, Convergence of derivatives for certain mixed Szász-Beta operators, J. Math. Anal. Appl. 321, 1–9, 2006.
  • [8] G.C. Jain, Approximation of functions by a new class of linear operators, J. Aust. Math. Soc. 13 (3), 271–276, 1972.
  • [9] A.S. Kumar and T. Acar, Approximation by generalized Baskakov-Durrmeyer-Stancu type operators, Rend. Circ. Mat. Palermo, Series 2, 65 (3), 411–424, 2016.
  • [10] G.G. Lorentz, Approximation of functions, Holt, Rinehart and Winston, Inc., New York, 1966.
  • [11] G.G. Lorentz, Bernstein Polynomials, 2nd Ed., Chelsea Publ. Comp., New York, NY, 1986.
  • [12] G. Mastroianni, Su un operatore lineare e positivo, Rend. Acc. Sc. Fis. Mat. Napoli, 46, 161,-176, 1979.
  • [13] C.A. Micchelli, Saturation classes and iterates of operators, Dissertation, Stanford, 1969.
  • [14] M. Mursaleen and M. Nasiruzzaman, Approximation of modified Jakimovski-Leviatan- Beta type operators, Constr. Math. Anal. 1 (2), 88–98, 2018.
  • [15] P.C. Sikkema, On some linear positive operators, Indag. Math. 32, 327–337, 1970.
  • [16] S. Tarabie, On Jain-Beta linear operators, Appl. Math. Inform. Sci. 6 (2), 213–216, 2012.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Octavian Agratını 0000-0002-2406-4274

Publication Date June 2, 2020
Published in Issue Year 2020 Volume: 49 Issue: 3

Cite

APA Agratını, O. (2020). Linear positive operators constructed by using Beta-type bases. Hacettepe Journal of Mathematics and Statistics, 49(3), 1030-1038. https://doi.org/10.15672/hujms.549015
AMA Agratını O. Linear positive operators constructed by using Beta-type bases. Hacettepe Journal of Mathematics and Statistics. June 2020;49(3):1030-1038. doi:10.15672/hujms.549015
Chicago Agratını, Octavian. “Linear Positive Operators Constructed by Using Beta-Type Bases”. Hacettepe Journal of Mathematics and Statistics 49, no. 3 (June 2020): 1030-38. https://doi.org/10.15672/hujms.549015.
EndNote Agratını O (June 1, 2020) Linear positive operators constructed by using Beta-type bases. Hacettepe Journal of Mathematics and Statistics 49 3 1030–1038.
IEEE O. Agratını, “Linear positive operators constructed by using Beta-type bases”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 3, pp. 1030–1038, 2020, doi: 10.15672/hujms.549015.
ISNAD Agratını, Octavian. “Linear Positive Operators Constructed by Using Beta-Type Bases”. Hacettepe Journal of Mathematics and Statistics 49/3 (June 2020), 1030-1038. https://doi.org/10.15672/hujms.549015.
JAMA Agratını O. Linear positive operators constructed by using Beta-type bases. Hacettepe Journal of Mathematics and Statistics. 2020;49:1030–1038.
MLA Agratını, Octavian. “Linear Positive Operators Constructed by Using Beta-Type Bases”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 3, 2020, pp. 1030-8, doi:10.15672/hujms.549015.
Vancouver Agratını O. Linear positive operators constructed by using Beta-type bases. Hacettepe Journal of Mathematics and Statistics. 2020;49(3):1030-8.