scholarly journals A Kantorovich Type of Szasz Operators Including Brenke-Type Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Fatma Taşdelen ◽  
Rabia Aktaş ◽  
Abdullah Altın
Keyword(s):  
Modulus Of Continuity ◽  
Order Of Convergence ◽  
Classical Approach ◽  
Type Result ◽  
Convergence Properties ◽  
Szász Operators ◽  
Korovkin’S Theorem ◽  
Second Modulus Of Continuity

We give a Kantorovich variant of a generalization of Szasz operators defined by means of the Brenke-type polynomials and obtain convergence properties of these operators by using Korovkin's theorem. We also present the order of convergence with the help of a classical approach, the second modulus of continuity, and Peetre's -functional. Furthermore, an example of Kantorovich type of the operators including Gould-Hopper polynomials is presented and Voronovskaya-type result is given for these operators including Gould-Hopper polynomials.

scholarly journals On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Sezgin Sucu ◽  
Gürhan İçöz ◽  
Serhan Varma
Keyword(s):  
Convergence Theorem ◽  
Quantitative Estimation ◽  
Laguerre Polynomials ◽  
Classical Approach ◽  
Type Result ◽  
Linear Positive Operators ◽  
Approximation Process ◽  
Charlier Polynomials ◽  
Szász Operators ◽  
Second Modulus Of Continuity

This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould-Hopper polynomials are given. Moreover, a Voronovskaya-type result is obtained for the operators containing Gould-Hopper polynomials.

scholarly journals Approximation by generalized Stancu type integral operators involving Sheffer polynomials

2018 ◽  
Vol 34 (2) ◽  
pp. 215-228
Author(s):  
M. MURSALEEN ◽  
◽  
SHAGUFTA RAHMAN ◽  
KHURSHEED J. ANSARI ◽  
◽  
...  
Keyword(s):  
Modulus Of Continuity ◽  
Integral Operators ◽  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Weighted Modulus Of Continuity ◽  
Type Integral ◽  
Weighted Modulus ◽  
Sheffer Polynomials ◽  
Korovkin’S Theorem

In this article, we give a generalization of integral operators which involves Sheffer polynomials introduced by Sucu and Buy¨ ukyazici. We obtain approximation properties of our operators with the help of the univer- ¨ sal Korovkin’s theorem and study convergence properties by using modulus of continuity, the second order modulus of smoothness and Peetre’s K-functional. We have also established Voronovskaja type asymptotic formula. Furthermore, we study the convergence of these operators in weighted spaces of functions on the positive semi-axis and estimate the approximation by using weighted modulus of continuity.

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 a generalized class of Dunkl type Szász operators based on post quantum calculus

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Abdullah Alotaibi
Keyword(s):  
Modulus Of Continuity ◽  
Maximal Functions ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Type Result ◽  
Quantum Calculus ◽  
Szász Operators

Abstract The main purpose of this paper is to introduce a generalized class of Dunkl type Szász operators via post quantum calculus on the interval $[ \frac{1}{2},\infty )$ [ 1 2 , ∞ ) . This type of modification allows a better estimation of the error on $[ \frac{1}{2},\infty ) $ [ 1 2 , ∞ ) rather than $[ 0,\infty )$ [ 0 , ∞ ) . We establish Korovkin type result in weighted spaces and also study approximation properties with the help of modulus of continuity of order one, Lipschitz type maximal functions, and Peetre’s K-functional. Furthermore, we estimate the degrees of approximations of the operators by modulus of continuity of order two.

scholarly journals Approximation by a power series summability method of Kantorovich type Szász operators including Sheffer polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Valdete Loku ◽  
Naim L. Braha ◽  
Toufik Mansour ◽  
M. Mursaleen
Keyword(s):  
Power Series ◽  
Summability Method ◽  
Approximation Properties ◽  
Type Result ◽  
Szász Operators ◽  
Sheffer Polynomials

AbstractThe main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.

The Dunkl generalization of Stancu type q-Szasz-Mirakjan-Kantorovich operators and some approximation results

2018 ◽  
Vol 34 (3) ◽  
pp. 363-370
Author(s):  
M. MURSALEEN ◽  
◽  
MOHD. AHASAN ◽  
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Exponential Function ◽  
Second Order ◽  
Lipschitz Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
Kantorovich Operators ◽  
Korovkin’S Theorem

In this paper, a Dunkl type generalization of Stancu type q-Szasz-Mirakjan-Kantorovich positive linear operators ´ of the exponential function is introduced. With the help of well-known Korovkin’s theorem, some approximation properties and also the rate of convergence for these operators in terms of the classical and second-order modulus of continuity, Peetre’s K-functional and Lipschitz functions are investigated.

scholarly journals Dunkl generalization of q-Szász-Mirakjan operators which preserve x2

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 733-747 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Shagufta Rahman
Keyword(s):  
Modulus Of Continuity ◽  
Exponential Function ◽  
Type Theorem ◽  
Convergence Properties ◽  
Voronovskaja Type Theorem

In the present paper we construct q-Sz?sz-Mirakjan operators generated by Dunkl generalization of the exponential function which preserve x2. We obtain some approximation results via universal Korovkin?s type theorem for these operators and study convergence properties by using the modulus of continuity. Furthermore, we obtain a Voronovskaja type theorem for these operators.

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 On the simultaneous improving k inclusion disks for polynomial zeros

Filomat ◽  
2008 ◽  
Vol 22 (2) ◽  
pp. 9-21
Author(s):  
Dusan Milosevic ◽  
Miodrag Petkovic
Keyword(s):  
Iterative Method ◽  
Order Of Convergence ◽  
Convergence Properties ◽  
Polynomial Zeros ◽  
Numerical Examples ◽  
Modified Method

A modification of the iterative method of B?rsch-Supan type for the simultaneous inclusion of polynomial zeros is considered. The modified method provides the simultaneous inclusion of k (of n ? k) zeros, dealing with k inclusion disks of these zeros and the point (unchangeable) approximations to the remaining n - k zeros. It is proved that the R-order of convergence of the considered method is two if k < n and three if k = n. Three numerical examples are given to illustrate convergence properties of the presented method. .

scholarly journals On a Durrmeyer-type modification of the Exponential sampling series

2020 ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini
Keyword(s):  
Asymptotic Formula ◽  
Uniform Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Convergence Properties ◽  
Sampling Series ◽  
Quantitative Results ◽  
Uniformly Continuous

Abstract In this paper we introduce the exponential sampling Durrmeyer series. We discuss pointwise and uniform convergence properties and an asymptotic formula of Voronovskaja type. Quantitative results are given, using the usual modulus of continuity for uniformly continuous functions. Some examples are also described.

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