arXiv subjects

Naokant Deo

Publications and source records attributed to Naokant Deo.

5 recordsLinked to original sources

arXiv2025

Durrmeyer type operators linked with Boas-Buck type polynomials

The present article intends to introduce the sequence of Baskakov-Durrmeyer type operators linked with the generating functions of Boas-Buck type polynomials. After calculating the moments, including the limiting case of central moments of the constructed sequence of operators, in the subsequent sections, we estimate the convergence rate using the Ditzian-Totik modulus of smoothness and some convergence results in Lipchitz-type space.

math.CA↗

arXiv2024

Approximation by a new sequence of operators involving Laguerre polynomials

This paper offers a newly created integral approach for operators employing the orthogonal modified Laguerre polynomials and Păltănea basis. These operators approximate the functions over the interval $[0,\infty)$. Further, the moments are established for the proposed operators, and the universal Korovkin's theorem is used to derive the approximation properties of the operators. We examine convergence using a variety of analytical methods, including the Lipschitz class, Peetre's K-functional, the second-order modulus of smoothness, and the modulus of continuity. Moreover, an asymptotic formula associated with the Voronovskaja-type is established. The approximation is estimated through the weighted modulus of continuity, and convergence of the proposed operators in weighted spaces of functions is investigated as well. Ultimately, we employ numerical examples and visual representations to validate the theoretical findings.

math.FA↗

arXiv2023

Some Approximation Properties by Szász-P{ă}lt{ă}nea type Operators involving the Appell Polynomials of class $A^2$

This article contributes to the new summation of Szász operators with the help of Appell polynomials of class $A^{2}$. We verified Bohman-Korovkin's theorem and prove the convergence results like Lipschitz-type space, Voronvaskaja-type asymptotic formula, and modulus of continuity using the given operators. Furthermore, we have shown the weighted modulus of continuity and the derivative of bounded variation.

math.CA↗

arXiv2019

Rate of convergence of Gupta-Srivastava operators based on certain parameters

In the present paper, we consider the Bézier variant of the general family of Gupta-Srivastava operators \cite{GS:18}. For the proposed operators, we discuss the rate of convergence by using of Lipschitz type space, Ditzian-Totik modulus of smoothness, weighted modulus of continuity and functions of bounded variation.

math.CA↗

arXiv2016

Generalized Positive Linear Operators based on PED and IPED

The paper deals with generalized positive linear operators based on Pólya-Eggenberger distribution(PED) as well as inverse Pólya-Eggenberger distribution(IPED). Initially, we give the moments by using Stirling numbers of second kind and then establish direct results, convergence with the help of local and weighted approximation of proposed operators.

math.FA↗