scholarly journals Kantorovich-type operators associated with a variant of Jain operators

2021 ◽  
Vol 66 (2) ◽  
pp. 279-288
Author(s):  
Octavian Agratini ◽  
Ogun Dogru
Keyword(s):  
Second Order ◽  
Positive Operators ◽  
Moduli Of Smoothness ◽  
Integral Type ◽  
Linear Positive Operators ◽  
New Variant ◽  
Discrete Operators ◽  
Unbounded Intervals

"This note focuses on a sequence of linear positive operators of integral type in the sense of Kantorovich. The construction is based on a class of discrete operators representing a new variant of Jain operators. By our statements, we prove that the integral family turns out to be useful in approximating continuous signals de ned on unbounded intervals. The main tools in obtaining these results are moduli of smoothness of rst and second order, K-functional and Bohman- Korovkin criterion."

Iterative combinations for Srivastava–Gupta operators

2020 ◽  
pp. 2150108
Author(s):  
Prerna Maheshwari Sharma
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Simultaneous Approximation ◽  
Higher Order ◽  
Positive Operators ◽  
Integral Type ◽  
Linear Positive Operators ◽  
General Family ◽  
Special Cases

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.

Global smoothness preservation with second order modulus of smoothness

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
Gancho Tachev
Keyword(s):  
Modulus Of Smoothness ◽  
Second Order ◽  
Positive Operators ◽  
Bernstein Operator ◽  
Linear Positive Operators ◽  
Global Smoothness Preservation ◽  
Global Smoothness

AbstractWe establish the global smoothness preservation of a function f by the sequence of linear positive operators. Our estimate is in terms of the second order Ditzian-Totik modulus of smoothness. Application is given to the Bernstein operator.

scholarly journals Approximation Properties of Certain Summation Integral Type Operators

2015 ◽  
Vol 48 (1) ◽  
Author(s):  
P. Patel ◽  
Vishnu Narayan Mishra
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Positive Operators ◽  
Inverse Theorem ◽  
Approximation Properties ◽  
Integral Type ◽  
Linear Positive Operators ◽  
Direct Results

AbstractIn the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

scholarly journals Convergence Estimates for Gupta-Srivastava Operators

2021 ◽  
Vol 45 (5) ◽  
pp. 739-749
Author(s):  
DANYAL SOYBAŞ ◽  
◽  
NEHA MALIK
Keyword(s):  
Positive Operators ◽  
Linear Positive Operators ◽  
Type Approximation ◽  
Unbounded Interval ◽  
Discrete Operators ◽  
Convergence Estimates ◽  
The Difference

The Grüss-Voronovskaya-type approximation results for the modified Gupta-Srivastava operators are considered. Moreover, the magnitude of differences of two linear positive operators defined on an unbounded interval has been estimated. Quantitative type results are established as we initially obtain the moments of generalized discrete operators and then estimate the difference of these operators with the Gupta-Srivastava operators.

scholarly journals Convergence of integral operators based on different distributions

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2277-2287 ◽  
Author(s):  
Vijay Gupta ◽  
Danyal Soybaş
Keyword(s):  
Integral Operators ◽  
Positive Operators ◽  
Compact Interval ◽  
Integral Type ◽  
Linear Positive Operators ◽  
Binomial Distributions ◽  
Direct Results

We propose a new sequence of integral type operators, which is based on the Polya and the binomial distributions. Here we have considered the value f (0) explicitly. It is observed that such integral operators preserve only the constant functions. We establish some direct results for the new sequence of linear positive operators. In the last section, we propose the modified form and observe that the modified form provides better approximation in the compact interval [1/3, 1/2].

Approximation by Baskakov-Durrmeyer operators based on (p, q)-integers

2018 ◽  
Vol 68 (4) ◽  
pp. 897-906 ◽  
Author(s):  
Tuncer Acar ◽  
Ali Aral ◽  
Mohammad Mursaleen
Keyword(s):  
Rate Of Convergence ◽  
Gamma Function ◽  
Positive Operators ◽  
Lipschitz Class ◽  
Linear Positive Operators ◽  
Test Function ◽  
Durrmeyer Operators ◽  
Durrmeyer Type Operators ◽  
Unbounded Intervals

Abstract In the present paper, we introduce a new sequence of linear positive operators based on (p, q)-integers. To approximate functions over unbounded intervals, we introduce Baskakov-Durrmeyer type operators using the (p, q)-Gamma function. We investigate rate of convergence of new operators in terms of modulus of continuities and obtain their approximation behavior for the functions belonging to Lipschitz class. At the end, we present a modification of new operators preserving the test function x.

scholarly journals Approximation of functions with linear positive operators which fix {1, φ} and {1, φ2}

2020 ◽  
Vol 28 (3) ◽  
pp. 255-265
Author(s):  
Fuat Usta
Keyword(s):  
Positive Operators ◽  
Approximation Of Functions ◽  
Linear Positive Operators ◽  
Different Types ◽  
Unbounded Intervals

AbstractIn this manuscript, linear and positive operators described on bounded and unbounded intervals that fix the function sets {1, φ} and {1, φ2} such that φ ∈ C[0, 1] are presented. Then we present different types of operators by choosing different functions and values. Finally, Voronovskaya type theorems are given for this newly defined sequences of linear and positive operators.

scholarly journals Direct Estimates for Certain Integral Type Operators

2018 ◽  
Vol 11 (4) ◽  
pp. 958-975 ◽  
Author(s):  
Alok Kumar ◽  
Dipti Tapiawala ◽  
Lakshmi Narayan Mishra
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Positive Operators ◽  
Approximation Properties ◽  
Integral Type ◽  
Global Approximation ◽  
Linear Positive Operators

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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