Meenu Goyal - Academia.edu (original) (raw)

Papers by Meenu Goyal

Springer optimization and its applications, 2016

The goal of this chapter is to present a survey of the literature on approximation of functions o... more The goal of this chapter is to present a survey of the literature on approximation of functions of two variables by linear positive operators. We study the approximation properties of these operators in the space of functions of two variables, continuous on a compact set. We also discuss the convergence of the operators in a weighted space of functions of two variables and find the rate of this convergence by means of modulus of continuity.

Springer proceedings in mathematics & statistics, 2015

This paper is in continuation of our work on certain genuine hybrid operators in (Positivity (Und... more This paper is in continuation of our work on certain genuine hybrid operators in (Positivity (Under review)) [3]. First, we discuss some direct results in simultaneous approximation by these operators, e.g. pointwise convergence theorem, Voronovskaja-type theorem and an error estimate in terms of the modulus of continuity. Next, we estimate the rate of convergence for functions having a derivative that coincides a.e. with a function of bounded variation.

Bollettino Dell'unione Matematica Italiana, Sep 21, 2015

The aim of this paper is to present a Stancu type Kantorovich modification of q-Bernstein-Schurer... more The aim of this paper is to present a Stancu type Kantorovich modification of q-Bernstein-Schurer operators introduced by Muraru (Mathematica LVI 2:1–11, 2011) and modified by Ren and Zeng (Bull Korean Math Soc 50(4):1145–1156, 2013). Here, we obtain a convergence theorem by using the well known Bohman-Korovkin criterion and find the estimate of the rate of convergence by means of modulus of continuity and Lipschitz function for these operators. Also, we establish a Korovkin type A-statistical approximation theorem.

Applied Mathematics and Computation, Feb 1, 2016

The purpose of this paper is to obtain some direct results for the Durrmeyer variant of q - Berns... more The purpose of this paper is to obtain some direct results for the Durrmeyer variant of q - Bernstein-Schurer operators for functions of one variable introduced by Acu et?al. 1. We also propose to study the bivariate extension of these operators and discuss the rate of convergence by using the modulus of continuity, the degree of approximation for the Lipschitz class of functions and the Voronovskaja type asymptotic theorem. Furthermore, we show the convergence of the operators by illustrative graphics in Maple to certain functions in both one and two dimensional cases.

Bollettino Dell'unione Matematica Italiana, Dec 14, 2015

In this paper, we introduce the Bèzier variant of the generalized Baskakov Kantorovich operators.... more In this paper, we introduce the Bèzier variant of the generalized Baskakov Kantorovich operators. We establish a direct approximation theorem with the aid of the Ditzian-Totik modulus of smoothness and also study the rate of convergence for the functions having a derivative of bounded variation for these operators.

Applied Mathematics and Computation, Nov 1, 2015

We introduce a one parameter family of hybrid operators and study quantitative convergence theore... more We introduce a one parameter family of hybrid operators and study quantitative convergence theorems for these operators e.g. local and weighted approximation results and simultaneous approximation of derivatives. Further, we discuss the statistical convergence of these operators. Lastly, we show the rate of convergence of these operators to a certain function by illustrative graphics in Matlab.

arXiv (Cornell University), Aug 6, 2018

In this article we present the Durrmeyer variant of generalized Bernstein operators that preserve... more In this article we present the Durrmeyer variant of generalized Bernstein operators that preserve the constant functions involving non-negative parameter ρ. We derive the approximation behaviour of these operators including global approximation theorem via Ditzian-Totik modulus of continuity, the order of convergence for the Lipschitz type space. Furthermore, we study a Voronovskaja type asymptotic formula and local approximation theorem by means of second order modulus of smoothness. Furthermore, we obtain the rate of approximation for absolutely continuous functions having a derivative equivalent with a function of bounded variation. In the last section of the article, we illustrate the convergence of these operators for certain functions using Maple software.

Annali Dell'universita' Di Ferrara, Jun 8, 2017

In this paper, we introduce the Bézier variant of the Jakimovski-Leviatan-Pȃltȃnea operators base... more In this paper, we introduce the Bézier variant of the Jakimovski-Leviatan-Pȃltȃnea operators based on Appell polynomials. We establish some local results, a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness and also study the rate of convergence for the functions having a derivative of bounded variation for these operators.

$Research paper thumbnail of Approximation Of Function By <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi><mo>−</mo></mrow><annotation encoding="application/x-tex">\alpha-</annotation></semantics></math>α−Baskakov Durrmeyer Type Operators$

arXiv (Cornell University), Dec 25, 2020

In the present article, we deal with the overconvergence of the Szász-Durrmeyer-Chlodowsky operat... more 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, ∞).

arXiv (Cornell University), May 18, 2016

arXiv (Cornell University), May 22, 2015

$Research paper thumbnail of Better approximation of function by <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi><mo>−</mo></mrow><annotation encoding="application/x-tex">\alpha-</annotation></semantics></math>α−Bernstein-P\u{a}lt\u{a}nea operators$

arXiv (Cornell University), Jun 4, 2020

In the present article, we deal with the overconvergence of the Sz?asz-Durrmeyer-Chlodowsky opera... more In the present article, we deal with the overconvergence of the Sz?asz-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 Sz?asz-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,\infty).

Mathematical Analysis, Approximation Theory and Their Applications, 2016

In this note, we introduce the Durrmeyer variant of Stancu operators that preserve the constant f... more In this note, we introduce the Durrmeyer variant of Stancu operators that preserve the constant functions depending on non-negative parameters. We give a global approximation theorem in terms of the Ditzian-Totik modulus of smoothness, a Voronovskaja type theorem and a local approximation theorem by means of second order modulus of continuity. Also, we obtain the rate of approximation for absolutely continuous functions having a derivative equivalent with a function of bounded variation. Lastly, we compare the rate of approximation of the Stancu-Durrmeyer operators and genuine Bernstein-Durrmeyer operators to certain function by illustrative graphics with the help of the Mathematica software.

arXiv: Classical Analysis and ODEs, 2015

This paper is in continuation of our work in \cite{PNM}, wherein we introduced generalized Baskak... more This paper is in continuation of our work in \cite{PNM}, wherein we introduced generalized Baskakov Kantorovich operators Kna(f;x)K_n^a(f;x)Kna(f;x) and established some approximation properties e.g. local approximation, weighted approximation, simultaneous approximation and A−A-A−statistical convergence. Also, we discussed the rate of convergence for functions having a derivative coinciding a.e. with a function of bounded variation. The purpose of this paper is to study the bivariate extension of the operators Kna(f;x)K_n^a(f;x)Kna(f;x) and discuss results on the degree of approximation, Voronovskaja type theorems and their first order derivatives in polynomial weighted spaces.

In the present article, we deal with the overconvergence of the Szasz-Durrmeyer-Chlodowsky operat... more In the present article, we deal with the overconvergence of the Szasz-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 Szasz-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 (0,1).

In the present note, we give the generalization of α−Baskakov Durrmeyer operators depending on a ... more In the present note, we give the generalization of α−Baskakov Durrmeyer operators depending on a real parameter ρ > 0. We present the approximation results in Korovkin and weighted Korovkin spaces. We also prove the order of approximation, rate of approximation for these operators. In the end, we verify our results with the help of numerical examples by using Mathematica.