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Papers by Dr. Sangeeta Garg

IMPACT, 2015

In the present paper we study about the Stancu variants of modified Beta operators. We obtain som... more In the present paper we study about the Stancu variants of modified Beta operators. We obtain some direct results in simultaneous approximation and asymptotic formula for these operators. We also modify these operators so as to preserve the linear moments, by applying the King's approach.

IMPACT , 2015

Journal of advances in mathematics and computer science, May 2, 2023

This research paper is an introduction to a new type of analogue named as-analogue for well-known... more This research paper is an introduction to a new type of analogue named as-analogue for well-known Baskakov Durrmeyer operators. This new type of analogue is considered as reverse order of-analogue. In this paper, we establish the direct approximation theorem, a weighted approximation theorem followed by the estimations of the rate of convergence of these new type of operators for functions of polynomial growth on the interval .

In this paper, we discuss the generalization of Szasz-Mirakyan-Baskakov type operators defined in... more In this paper, we discuss the generalization of Szasz-Mirakyan-Baskakov type operators defined in [7], using the iterative combinations in ordinary and simultaneous approximations. We have better estimates in higher order modulus of continuity for these operators in simultaneous approximation.

CRC Press eBooks, Oct 26, 2022

Publications de l'Institut Math?matique (Belgrade)

Recently Indian known mathematician V. Gupta introduced a general family of linear positive opera... more Recently Indian known mathematician V. Gupta introduced a general family of linear positive operators, which produces a large number of well-known linear positive operators as particular cases. The family of operators, proposed by Gupta provides a unified approach. This motivated us to extend the studies and we establish some convergence estimates which include an asymptotic formula and the rate of convergence for the function having derivatives of bounded variation.

International Journal of Innovative Technology and Exploring Engineering, 2020

The paper is some proposal of advance properties of Beta-Baskakov-Stancu operators consisting hyp... more The paper is some proposal of advance properties of Beta-Baskakov-Stancu operators consisting hypergeo-metric series function. The central moments, Voronovskaya type asymptotic formula and error estimates applying some characteristic properties are obtained for mentioned operators.

Recently, many researchers have concerned the problems based on difference of two linear positive... more Recently, many researchers have concerned the problems based on difference of two linear positive operators having same basis functions. In this paper, we deal with the difference of two summation integral type linear positive operators, one having different basis functions and other Durrmeyer type operators. We also obtained the difference of Baskakov operators and beta operators.

Global Journal of Pure and Applied Mathematics, 2015

In the present paper, we extend our study for modified Baskakov operators defined by Gupta-Srivas... more In the present paper, we extend our study for modified Baskakov operators defined by Gupta-Srivastava [5]. We introduce modified Baskakov-Stancu type operators and give the moments in terms of hypergeometric series functions. Further, we establish asymptotic formula and error estimation in simultaneous approximation for these operators.

Current Topics on Mathematics and Computer Science Vol. 4, 2021

The word approximation is derived from Latin word “approximatus”. The term can be applied in our ... more The word approximation is derived from Latin word “approximatus”. The term can be applied in our surroundings to various properties (e.g. value, quantity, image, description) that are nearly, but not exactly correct or similar, but not exactly the same. Mostly approximation is often applied to numbers but it is also frequently applied to such things as mathematical functions, shapes, and physical laws [1,2]. In science, approximation can refer to use a simpler process or model when the correct model is difficult to use. An approximate model is used to make calculations easier. Approximations might also be used if incomplete information prevents use of exact representations. The type of approximation depends on the available information, the degree of accuracy, sensitivity of the problem to the data and the savings (usually in time and effort). In this chapter, we present a systematic overview of approximation by the use of linear positive operators, a useful tool used to increase the order of approximation [2]. The properties of operators are not only limited to the functions of bounded variation but unbounded variation also [3]. Many authors studied and used the rate of convergence, Moduli of smoothness etc. to get various results for several operators. Here we use summation-integral type linear positive operators to approximate an unbounded function. These operators can be named as Dual Beta type operators. We obtain moments and other type of results in simultaneous approximation and Voronovskaya type asymptotic formula for this new sequence of operators. We also find important direct theorem for these operators.

This paper deals with Stancu type generalization of q-analogue of Baskakov-Szasz operators introd... more This paper deals with Stancu type generalization of q-analogue of Baskakov-Szasz operators introducing a new sequence of positive q-integral operators. We show that it is a weighted approximation process in the polynomial space of continuous functions defined on [0, ∞). An estimate for the rate of convergence and weighted approximation properties are also obtained for these operators.