Approximation of General Form for a Sequence of Linear Positive Operators Based on Four Parameters
DOI:
https://doi.org/10.24297/jam.v14i2.7573Keywords:
Sequences based on parameters, Korovkin theorem, m-th order moment, Voronovaskaja –type asymptotic formula, Simultaneous ApproximationAbstract
In the present paper, we define a generalization sequence of linear positive operators based on four parameters which is reduce to many other sequences of summation–integral older type operators of any weight function (Bernstein, Baskakov, Szász or Beta). Firstly, we find a recurrence relation of the -th order moment and study the convergence theorem for this generalization sequence. Secondly, we give a Voronovaskaja-type asymptotic formula for simultaneous approximation. Finally, we introduce some numerical examples to view the effect of the four parameters of this sequence.
Downloads
References
A.J. Mohammad and A. K. Hassan, A generalization of Baskakov operators of summation-integral- Phillips type form, Basrah J. of Sci. vol. 31(1), 28-40, (2013).
D. Soybas, Approximation with modified Phillips operators, J. Nonlinear Sci. Appl., 10, 5803–5812 (2017).
E.E. Berdysheva, Operators of Durrmeyer type with respect to arbitrary measure, Springer Proceeding in Mathematics & Statistics, Roorkee, India, Dec. (2014).
H.M. Srivastava and V. Gupta, A certain family of summation-integral type operators. Math. Comput. Model.37, 1307–1315 (2003).
M. Goyal and P.N. Agrawal, Degree of approximation by certain genuine hybrid operators, Springer Proceeding in Mathematics & Statistics, Roorkee, India, Dec. (2014).
M. Heilmann and I. Rasa, k th order Kantorovich modification of linking Baskakov-type operators, Springer Proceeding in Mathematics & Statistics, Roorkee, India, Dec. (2014).
P.P. Korovkin: Linear Operators and Approximation Theory, Hindustan publ. Corp. Delhi, 1960 (Translated from Russian Edition) (1959).
R. Paltanea, Modified Szász-Mirakjan operators of integral form, Carpathian J. Math. 24 (2008), 378-385.
R.P. Sinha, P.N. Agrawal and V. Gupta, On simultaneous approximation by modified Baskakov operators, Bull. Soc. Math. Belg. 43, 217–231 (1991).
S.M. Mazhar and V. Totik, Approximation by modified Szász operators, Acra Sci. Math, 49, 257-269 (1985).
V. Cupta, M. Rassisas, P.N. Agrawal and M. Goyal, Approximation with certain genuine hybrid operators, Serbia N. of Sci (2017).
V. Gupta and G.S. Srivastava, Simultaneous approximation by Baskakov–Szász type operators, Bull. Soc. math, tome 37(85), nr 3-4 (1993).
V. Gupta and S. Srivastava, Convergence of derivatives by summation-integral type operators, math, India, (1995).
Downloads
Published
How to Cite
Issue
Section
License
All articles published in Journal of Advances in Linguistics are licensed under a Creative Commons Attribution 4.0 International License.
