scholarly journals Determination of the exact degree of local approximation by some linear positive operators involving the modulus of continuity of the p-th derivative

1981 ◽  
Vol 84 (1) ◽  
pp. 117-128 ◽  
Author(s):  
P.C. Sikkema ◽  
P.J.C. van der Meer ◽  
Maria Roos
Author(s):  
Prerna Maheshwari Sharma

In the year 2003, Srivastava–Gupta proposed a general family of linear positive operators, having some well-known operators as special cases. They investigated and established the rate of convergence of these operators for bounded variations. In the last decade for modified form of Srivastava–Gupta operators, several other generalizations also have been discussed. In this paper, we discuss the generalized modified Srivastava–Gupta operators considered in [H. M. Srivastava and V. Gupta, A certain family of summation-integral type operators, Math. Comput. Modelling 37(12–13) (2003) 1307–1315], by using iterative combinations in ordinary and simultaneous approximation. We may have better approximation in higher order of modulus of continuity for these operators.


2020 ◽  
Vol 17 (3) ◽  
pp. 0882
Author(s):  
Saheb AL- Saidy ◽  
Naseif AL-Jawari ◽  
Ali Hussein Zaboon

The purpose of this paper is to find the best multiplier approximation of unbounded functions in    –space by using some discrete linear positive operators. Also we will estimate the degree of the best multiplier approximation in term of modulus of continuity and the averaged modulus.


Analysis ◽  
2020 ◽  
Vol 40 (4) ◽  
pp. 163-173
Author(s):  
Lakshmi Narayan Mishra ◽  
Shikha Pandey ◽  
Vishnu Narayan Mishra

AbstractApproximation using linear positive operators is a well-studied research area. Many operators and their generalizations are investigated for their better approximation properties. In the present paper, we construct and investigate a variant of modified (p,q)-Baskakov operators, which reproduce the test function x^{2}. We have determined the order of approximation of the operators via K-functional and second order, the usual modulus of continuity, weighted and statistical approximation properties. In the end, some graphical results which depict the comparison with (p,q)-Baskakov operators are explained and a Voronovskaja type result is obtained.


2007 ◽  
Vol 44 (1) ◽  
pp. 65-80 ◽  
Author(s):  
Mehmet Özarslan

The main object of this paper is to define the q -Laguerre type positive linear operators and investigate the approximation properties of these operators. The rate of convegence of these operators are studied by using the modulus of continuity, Peetre’s K -functional and Lipschitz class functional. The estimation to the difference | Mn +1, q ( ƒ ; χ )− Mn , q ( ƒ ; χ )| is also obtained for the Meyer-König and Zeller operators based on the q -integers [2]. Finally, the r -th order generalization of the q -Laguerre type operators are defined and their approximation properties and the rate of convergence of this r -th order generalization are also examined.


2004 ◽  
Vol 41 (4) ◽  
pp. 415-429 ◽  
Author(s):  
O. Doğru ◽  
M. A. Özarslan ◽  
F. Taşdelen

In this paper we introduced the general sequence of linear positive operators via generating functions. Approximation properties of these operators are obtained with the help of the Korovkin Theorem. The order of convergence of these operators computed by means of modulus of continuity Peetre’s K-furictiorial and the elements of the usual Lipschitz class. Also we introduce the r-th order generalization of these operators and we evaluate this generalization by the operators defined in this paper. Finally we give some applications to differential equations.


2018 ◽  
Vol 11 (4) ◽  
pp. 958-975 ◽  
Author(s):  
Alok Kumar ◽  
Dipti Tapiawala ◽  
Lakshmi Narayan Mishra

In this note, we study approximation properties of a family of linear positive operators and establish asymptotic formula, rate of convergence, local approximation theorem, global approximation theorem, weighted approximation theorem, and better approximation for this family of linear positive operators.


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