Year 2020, Volume 49 , Issue 3, Pages 1030 - 1038 2020-06-02

Linear positive operators constructed by using Beta-type bases

Octavian AGRATINI [1]


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.
Korovkin theorem, modulus of smoothness, weighted space, rate of convergence
  • [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.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-2406-4274
Author: Octavian AGRATINI (Primary Author)
Institution: BABEŞ-BOLYAİ UNIVERSITY
Country: Romania


Dates

Publication Date : June 2, 2020

Bibtex @research article { hujms549015, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1030 - 1038}, doi = {10.15672/hujms.549015}, title = {Linear positive operators constructed by using Beta-type bases}, key = {cite}, author = {Agratını, Octavian} }
APA Agratını, O . (2020). Linear positive operators constructed by using Beta-type bases . Hacettepe Journal of Mathematics and Statistics , 49 (3) , 1030-1038 . DOI: 10.15672/hujms.549015
MLA Agratını, O . "Linear positive operators constructed by using Beta-type bases" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1030-1038 <https://dergipark.org.tr/en/pub/hujms/issue/54699/549015>
Chicago Agratını, O . "Linear positive operators constructed by using Beta-type bases". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1030-1038
RIS TY - JOUR T1 - Linear positive operators constructed by using Beta-type bases AU - Octavian Agratını Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.549015 DO - 10.15672/hujms.549015 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1030 EP - 1038 VL - 49 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.549015 UR - https://doi.org/10.15672/hujms.549015 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Linear positive operators constructed by using Beta-type bases %A Octavian Agratını %T Linear positive operators constructed by using Beta-type bases %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 3 %R doi: 10.15672/hujms.549015 %U 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
AMA Agratını O . Linear positive operators constructed by using Beta-type bases. Hacettepe Journal of Mathematics and Statistics. 2020; 49(3): 1030-1038.
Vancouver Agratını O . Linear positive operators constructed by using Beta-type bases. Hacettepe Journal of Mathematics and Statistics. 2020; 49(3): 1030-1038.