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].

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.

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.

On the rate of convergence of some integral operators for functions of bounded variation

2005 ◽  
Vol 42 (2) ◽  
pp. 235-252
Author(s):  
Octavian Agratini
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
General Class ◽  
Pointwise Convergence ◽  
Integral Operators ◽  
Positive Operators ◽  
Functions Of Bounded Variation ◽  
Linear Positive Operators ◽  
The One

In the present paper we define a general class Bn,a, a =1, of Durrmeyer-Bézier type of linear positive operators. Our main aim is to estimate the rate of pointwise convergence for functions f at those points x at which the one-sided limits f(x+) and f(x-) exist. As regards these functions defined on an interval J certain conditions are required. We discuss two distinct cases: Int (J)=(0,8) and Int (J)=(0,1).

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."

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.

On the approximation of convex functions using linear positive operators

2017 ◽  
Vol 26 (2) ◽  
pp. 137-143
Author(s):  
DAN BARBOSU
Keyword(s):  
Convex Functions ◽  
Remainder Term ◽  
Mean Value ◽  
Positive Operators ◽  
Linear Functionals ◽  
Linear Positive Operators ◽  
Famous Theorem ◽  
Approximation Formulas ◽  
Phd Thesis ◽  
Higher Order Convexity

The goal of the paper is to present some results concerning the approximation of convex functions by linear positive operators. First, one recalls some results concerning the univariate real valued convex functions. Next, one presents the notion of higher order convexity introduced by Popoviciu [Popoviciu, T., Sur quelques propri´et´ees des fonctions d’une ou deux variable r´eelles, PhD Thesis, La Faculte des Sciences de Paris, 1933 (June)] . The Popoviciu’s famous theorem for the representation of linear functionals associated to convex functions of m−th order (with the proof of author) is also presented. Finally, applications of the convexity to study the monotonicity of sequences of some linear positive operators and also mean value theorems for the remainder term of some approximation formulas based on linear positive operators are presented.

Inverse theorems for some linear positive operators using Beta and Baskakov basis functions

2021 ◽  
Author(s):  
Lakshmi Narayan Mishra ◽  
A. Srivastava ◽  
T. Khan ◽  
S. A. Khan ◽  
Vishnu Narayan Mishra
Keyword(s):  
Positive Operators ◽  
Basis Functions ◽  
Linear Positive Operators ◽  
Inverse Theorems
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