scholarly journals Stancu-type generalizations of the Chan-Chyan-Srivastava operators

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3733-3742 ◽  
Author(s):  
Gürhan İçöz ◽  
Bayram Çekim
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Modulus Of Smoothness ◽  
Lipschitz Class ◽  
Type Result ◽  
Approximation Theorems

We give the Stancu-type generalization of the operators which is given by Erkus-Duman and Duman in this study. We derive approximation theorems via A-statistical Korovkin-type result. We also give rate of convergence of the operators via the modulus of smoothness, the modulus of continuity, and Lipschitz class functional.

scholarly journals Dunkl-type generalization of the second kind beta operators via $(p,q)$-calculus

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Md. Nasiruzzaman ◽  
Abdullah Alotaibi ◽  
M. Mursaleen
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Lipschitz Class ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Research Article ◽  
Local Approximations ◽  
Korovkin Type Approximation Theorems

AbstractThe main purpose of this research article is to construct a Dunkl extension of $(p,q)$ ( p , q ) -variant of Szász–Beta operators of the second kind by applying a new parameter. We obtain Korovkin-type approximation theorems, local approximations, and weighted approximations. Further, we study the rate of convergence by using the modulus of continuity, Lipschitz class and Peetre’s K-functionals.

scholarly journals Approximation by Parametric Extension of Szász-Mirakjan-Kantorovich Operators Involving the Appell Polynomials

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Md. Nasiruzzaman ◽  
A. F. Aljohani
Keyword(s):  
Rate Of Convergence ◽  
Weighted Space ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Appell Polynomials ◽  
Global Approximation ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Dunkl Analogue ◽  
Kantorovich Operators

The purpose of this article is to introduce a Kantorovich variant of Szász-Mirakjan operators by including the Dunkl analogue involving the Appell polynomials, namely, the Szász-Mirakjan-Jakimovski-Leviatan-type positive linear operators. We study the global approximation in terms of uniform modulus of smoothness and calculate the local direct theorems of the rate of convergence with the help of Lipschitz-type maximal functions in weighted space. Furthermore, the Voronovskaja-type approximation theorems of this new operator are also presented.

scholarly journals Stancu-variant of generalized Baskakov operators

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2625-2632 ◽  
Author(s):  
Nadeem Rao ◽  
Abdul Wafi
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Order Of Approximation ◽  
Baskakov Operators ◽  
Direct Estimate ◽  
Voronovskaya Type Theorem

In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.

scholarly journals Some approximation results for (p,q)-Lupaş-Schurer operators

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 217-229 ◽  
Author(s):  
K. Kanat ◽  
M. Sofyalıoğlu
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Approximation Theorem ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation

In this paper, we introduce Lupa?-Schurer operators based on (p,q)-integers. Then, we deal with the approximation properties for (p,q)-Lupa?-Schurer operators based on Korovkin type approximation theorem. Moreover, we compute rate of convergence by using modulus of continuity, with the help of functions of Lipschitz class and Peetre?s K-functionals.

scholarly journals Approximation properties of (p;q)-variant of Stancu-Schurer operators

2018 ◽  
Vol 37 (4) ◽  
pp. 137-151 ◽  
Author(s):  
Abdul Wafi ◽  
Nadeem Rao ◽  
_ Deepmala
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Second Order ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Direct Approximation ◽  
Korovkin Type Theorems

In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates, Korovkin-type theorems and direct approximation results using second order modulus of continuity, Peetre’s K-functional and Lipschitz class.

scholarly journals Approximation by q-analogue of modified Jakimovski-Leviatan-Stancu type operators

2017 ◽  
Vol 50 (1) ◽  
pp. 175-189
Author(s):  
Mohammad Mursaleen ◽  
Mohammad Nasiruzzaman ◽  
Abdul Wafi
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Lipschitz Class ◽  
Convergence Properties ◽  
Korovkin’S Theorem

Abstract In this paper, we introduce the q-analogue of the Jakimovski-Leviatan type modified operators introduced by Atakut with the help of the q-Appell polynomials.We obtain some approximation results via the well-known Korovkin’s theorem for these operators.We also study convergence properties by using the modulus of continuity and the rate of convergence of the operators for functions belonging to the Lipschitz class. Moreover,we study the rate of convergence in terms of modulus of continuity of these operators in aweighted space.

scholarly journals Approximation by Bézier Variant of Baskakov-Durrmeyer-Type Hybrid Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lahsen Aharouch ◽  
Khursheed J. Ansari ◽  
M. Mursaleen
Keyword(s):  
Rate Of Convergence ◽  
Present Article ◽  
Bounded Variation ◽  
Modulus Of Continuity ◽  
Lipschitz Function ◽  
Modulus Of Smoothness ◽  
Weighted Modulus Of Continuity ◽  
Type Formula ◽  
Weighted Modulus ◽  
Bézier Variant

We give a Bézier variant of Baskakov-Durrmeyer-type hybrid operators in the present article. First, we obtain the rate of convergence by using Ditzian-Totik modulus of smoothness and also for a class of Lipschitz function. Then, weighted modulus of continuity is investigated too. We study the rate of point-wise convergence for the functions having a derivative of bounded variation. Furthermore, we establish the quantitative Voronovskaja-type formula in terms of Ditzian-Totik modulus of smoothness at the end.

q -Laguerre type linear positive operators

2007 ◽  
Vol 44 (1) ◽  
pp. 65-80 ◽  
Author(s):  
Mehmet Özarslan
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Positive Operators ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Linear Positive Operators ◽  
The Difference

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.

scholarly journals Kantrovich Type Generalization of Meyer-Konig and Zeller Operators via Generating Functions

2013 ◽  
Vol 21 (3) ◽  
pp. 209-222 ◽  
Author(s):  
Ali Olgun ◽  
H. Gül İnce ◽  
Fatma Tasdelen
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Generating Functions ◽  
Type Theorem ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Korovkin Type Theorem

Abstract In the present paper, we study a Kantorovich type generalization of Meyer-König and Zeller type operators via generating functions. Using Korovkin type theorem we first give approximation properties of these operators defined on the space C [0;A] ; 0 < A < 1. Secondly, we compute the rate of convergence of these operators by means of the modulus of continuity and the elements of the modified Lipschitz class. Finally, we give an r-th order generalization of these operators in the sense of Kirov and Popova and we obtain approximation properties of them.

Blending type approximation by generalized Szász type operators based on Charlier polynomials

2018 ◽  
Vol 27 (1) ◽  
pp. 49-56
Author(s):  
ARUN KAJLA ◽  
Keyword(s):  
Rate Of Convergence ◽  
Weighted Approximation ◽  
Type Result ◽  
Weighted Modulus Of Continuity ◽  
Charlier Polynomials ◽  
Weighted Function ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Weighted Function Space ◽  
Weighted Modulus

In the present paper, we introduce a generalized Szasz type operators based on ´ ρ(x) where ρ is a continuously differentiable function on [0, ∞), ρ(0) = 0 and inf ρ 0 (x) ≥ 1, x ∈ [0, ∞). This function not only characterizes the operators but also characterizes the Korovkin set 1, ρ, ρ2 in a weighted function space. First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then we obtain a Voronovskaja type result and the rate of convergence in terms of the weighted modulus of continuity.

Sign in / Sign up

Export Citation Format

Share Document