scholarly journals APPROXIMATION BY GENERALIZED q-SZASZ-MIRAKJAN ´ OPERATORS

2021 ◽  
Vol 12 (6) ◽  
pp. 9-21
Author(s):  
TAQSEER KHAN ◽  
MOHD SAIF ◽  
SHUZAAT ALI KHAN
Keyword(s):  
Approximation Properties ◽  
Quantitative Estimates ◽  
Voronovskaja’S Theorem

In this article, we introduce generalized q−Sz´asz-Mirakjan operators and study their approximation properties. Based on the Voronovskaja’s theorem, we obtain quantitative estimates for these operators.

Voronovskaja’s theorem, shape preserving properties and iterations for complex q-Bernstein polynomials

2011 ◽  
Vol 48 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Sorin Gal
Keyword(s):  
Convergence Theorem ◽  
Analytic Functions ◽  
Quantitative Estimate ◽  
Bernstein Polynomials ◽  
Exact Order ◽  
Approximation Properties ◽  
Shape Preserving ◽  
Voronovskaja’S Theorem ◽  
Shape Preserving Properties ◽  
Compact Disks

In this paper, first we prove Voronovskaja’s convergence theorem for complex q-Bernstein polynomials, 0 < q < 1, attached to analytic functions in compact disks in ℂ centered at origin, with quantitative estimate of this convergence. As an application, we obtain the exact order in approximation of analytic functions by the complex q-Bernstein polynomials on compact disks. Finally, we study the approximation properties of their iterates for any q > 0 and we prove that the complex qn-Bernstein polynomials with 0 < qn < 1 and qn → 1, preserve in the unit disk (beginning with an index) the starlikeness, convexity and spiral-likeness.

scholarly journals Exponential moments and simultaneous approximation properties for Durrmeyer type operators with weights of Szasz basis functions

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1465-1475
Author(s):  
Antonio-Jesús López-Moreno ◽  
Vijay Gupta
Keyword(s):  
Exponential Type ◽  
Exponential Growth ◽  
Simultaneous Approximation ◽  
Basis Functions ◽  
Approximation Properties ◽  
Exponential Functions ◽  
Quantitative Estimates ◽  
Exponential Moments ◽  
Durrmeyer Type Operators ◽  
Derivatives Of

The present paper deals with the approximation properties for exponential functions of general Durrmeyer type operators having the weights of Sz?sz basis functions. Here we give explicit expressions for exponential type moments by means of which we establish, for the derivatives of the operators, the Voronovskaja formulas for functions of exponential growth and the corresponding weighted quantitative estimates for the remainder in simultaneous approximation.

scholarly journals Approximation by the -Szász-Mirakjan Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
N. I. Mahmudov
Keyword(s):  
Weighted Spaces ◽  
Rate Of Approximation ◽  
Quantitative Estimates ◽  
Voronovskaja’S Theorem

This paper deals with approximating properties of theq-generalization of the Szász-Mirakjan operators in the case . Quantitative estimates of the convergence in the polynomial-weighted spaces and the Voronovskaja's theorem are given. In particular, it is proved that the rate of approximation by theq-Szász-Mirakjan operators ( ) is of order versus 1/nfor the classical Szász-Mirakjan operators.

scholarly journals Quantitative estimates for Szász operators and its hybrid variant

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1107-1114
Author(s):  
Ekta Pandey
Keyword(s):  
Asymptotic Formula ◽  
Present Article ◽  
Modulus Of Continuity ◽  
Approximation Properties ◽  
Weighted Modulus Of Continuity ◽  
Baskakov Operators ◽  
Szász Operators ◽  
Quantitative Estimates ◽  
Weighted Modulus

The present article deals with the study on approximation properties of well known Sz?sz-Mirakyan operators. We estimate the quantitative Voronovskaja type asymptotic formula for the Sz?sz-Baskakov operators and difference between Sz?sz-Mirakyan operators and the hybrid Sz?sz operators having weights of Baskakov basis in terms of the weighted modulus of continuity

Approximation by complex summation-integral type operator in compact disks

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
Vijay Gupta ◽  
Rani Yadav
Keyword(s):  
Complex Plane ◽  
Analytic Functions ◽  
Quantitative Estimate ◽  
Type Operator ◽  
Approximation Properties ◽  
Integral Type ◽  
Quantitative Estimates ◽  
Compact Disks ◽  
Durrmeyer Polynomials

AbstractIn the present paper we estimate a Voronovskaja type quantitative estimate for a certain type of complex Durrmeyer polynomials, which is different from those studied previously in the literature. Such estimation is in terms of analytic functions in the compact disks. In this way, we present the evidence of overconvergence phenomenon for this type of Durrmeyer polynomials, namely the extensions of approximation properties (with quantitative estimates) from real intervals to compact disks in the complex plane. In the end, we mention certain applications.

scholarly journals Quantitative estimates for the Lupaş q-analogue of the Bernstein operator

2011 ◽  
Vol 44 (1) ◽  
Author(s):  
Zoltán Finta
Keyword(s):  
Modulus Of Smoothness ◽  
Bernstein Operator ◽  
Approximation Properties ◽  
Global Approximation ◽  
Approximation Theorems ◽  
Quantitative Estimates ◽  
Quantitative Results

AbstractWe establish quantitative results for the approximation properties of the q-analogue of the Bernstein operator defined by Lupaş in 1987 and for the approximation properties of the limit Lupaş operator introduced by Ostrovska in 2006, via Ditzian-Totik modulus of smoothness. Our results are local and global approximation theorems.

scholarly journals Approximation properties of mixed sampling-Kantorovich operators

2020 ◽  
Vol 115 (1) ◽  
Author(s):  
Laura Angeloni ◽  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Uniform Convergence ◽  
Type Theorem ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Voronovskaja Type Theorem ◽  
Quantitative Estimates ◽  
Kantorovich Operators

Abstract In the present paper we study the pointwise and uniform convergence properties of a family of multidimensional sampling Kantorovich type operators. Moreover, besides convergence, quantitative estimates and a Voronovskaja type theorem have been established.

Blending type approximation by complex Szász-Durrmeyer-Chlodowsky operators in compact disks

2019 ◽  
Vol 69 (5) ◽  
pp. 1077-1088
Author(s):  
Meenu Goyal ◽  
P. N. Agrawal
Keyword(s):  
Analytic Functions ◽  
Simultaneous Approximation ◽  
Asymptotic Result ◽  
Exact Order ◽  
Approximation Properties ◽  
Type Result ◽  
Type Approximation ◽  
Quantitative Estimates ◽  
Compact Disks ◽  
Upper Estimate

Abstract In the present article, we deal with the overconvergence of the Szász-Durrmeyer-Chlodowsky operators. Here we study the approximation properties e.g. upper estimates, Voronovskaja type result for these operators attached to analytic functions in compact disks. Also, we discuss the exact order in simultaneous approximation by these operators and its derivatives and the asymptotic result with quantitative upper estimate. In such a way, we put in evidence the overconvergence phenomenon for the Szász-Durrmeyer-Chlodowsky operators, namely the extensions of approximation properties with exact quantitative estimates and orders of these convergencies to sets in the complex plane that contain the interval [0, ∞).

scholarly journals A new construction of Lupaş operators and its approximation properties

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohd Qasim ◽  
Asif Khan ◽  
Zaheer Abbas ◽  
Qing-Bo Cai
Keyword(s):  
Uniform Approximation ◽  
Type Theorem ◽  
Local Approximation ◽  
Moduli Of Smoothness ◽  
Approximation Properties ◽  
Quantitative Estimates ◽  
Voronovskaya Type Theorem ◽  
Lupaş Operators ◽  
New Construction ◽  
Weighted Moduli Of Smoothness

AbstractThe aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences $u_{m} $ u m and $v_{m}$ v m of functions. We prove that the new operators provide better weighted uniform approximation over $[0,\infty )$ [ 0 , ∞ ) . In terms of weighted moduli of smoothness, we obtain degrees of approximation associated with the function ρ. Also, we prove Voronovskaya-type theorem, quantitative estimates for the local approximation.

scholarly journals Approximation by Generalized Lupaş Operators Based on q-Integers

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 68 ◽  
Author(s):  
Mohd Qasim ◽  
M. Mursaleen ◽  
Asif Khan ◽  
Zaheer Abbas
Keyword(s):  
Local Approximation ◽  
Approximation Properties ◽  
Unbounded Function ◽  
Quantitative Estimates ◽  
Lupaş Operators ◽  
Selection Of

The purpose of this paper is to introduce q-analogues of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing, and unbounded function ρ . Depending on the selection of q, these operators provide more flexibility in approximation and the convergence is at least as fast as the generalized Lupaş operators, while retaining their approximation properties. For these operators, we give weighted approximations, Voronovskaja-type theorems, and quantitative estimates for the local approximation.

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