Prerna Sharma - Academia.edu (original) (raw)
Papers by Prerna Sharma
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.
Filomat, 2015
Very recently the modified form of Srivastava-Gupta operators was studied in order to preserve th... more Very recently the modified form of Srivastava-Gupta operators was studied in order to preserve the linear functions. Here, we estimate the rate of approximation for functions having bounded derivatives of the modified form.
gmj, 2006
In this paper we study the modified Beta operators. We extend the result of [Gupta and Ahmad, İst... more In this paper we study the modified Beta operators. We extend the result of [Gupta and Ahmad, İstanbul niv. Fen Fak. Mat. Derg. 54: 11–22 1995] and obtain an inverse result for the linear combination of these modified Beta operators in simultaneous approximation.
Demonstratio Mathematica, 2009
In the year 1993, Gupta and Srivastava [3] introduced the integral modification of the well known... more In the year 1993, Gupta and Srivastava [3] introduced the integral modification of the well known Baskakov operators by taking the weight functions of Szasz basis function, so called Baskakov-Szasz operators. In this paper, we obtain some direct theorems for the linear combination of these Baskakov Szasz type operators. To prove our one of the direct theorems, we use the technique of a mathematical tool which is the linear approximating method and is known as the Steklov means.
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.
International Journal of Mathematics and Mathematical Sciences, 2009
We establish the rate of convergence for the modified Beta operators , for functions having deriv... more We establish the rate of convergence for the modified Beta operators , for functions having derivatives of bounded variation.
International Journal of Mathematics and Mathematical Sciences, 2003
We obtain a converse theorem for the linear combinations of modified beta operators whose weight ... more We obtain a converse theorem for the linear combinations of modified beta operators whose weight function is the Baskakov operators. To prove our inverse theorem, we use the technique of linear approximating method, namely, Steklov mean.
Applied Mathematics E-Notes, 2007
In the present paper we obtain a saturation theorem for the linear combination of modified Beta o... more In the present paper we obtain a saturation theorem for the linear combination of modified Beta operators.
Demonstratio Mathematica, 2015
The applications of q-calculus in the approximation theory is a very interesting area of research... more The applications of q-calculus in the approximation theory is a very interesting area of research in the recent years, several new q-operators were introduced and their behaviour were discussed by many researchers. This paper is the extension of the paper [15], in which Durrmeyer type generalization of q-Baskakov-Stancu type operators were discussed by using the concept of q-integral operators. Here, we propose to study the Stancu variant of q-Baskakov-Stancu type operators. We establish an estimate for the rate of convergence in terms of modulus of continuity and weighted approximation properties of these operators.
Nepal Journal of Mathematical Sciences, 2021
This paper concerns with the study of(p, q)-analogue of genuine Baskakov-Durrmeyer type operators... more This paper concerns with the study of(p, q)-analogue of genuine Baskakov-Durrmeyer type operators. We establish the direct approximation theorem, a weighted approximation theorem followed by the estimations of the rate of convergence of these operators for functions of polynomial growth on the interval [)
Current Overview on Science and Technology Research Vol. 3
In this paper, we show the importance of Vedic mathematics to derive the optimal solution in agri... more In this paper, we show the importance of Vedic mathematics to derive the optimal solution in agriculture e.g. for soil management and crop production, sowing of seeds etc. Since the primary requirement of any being is food i.e. anna, a man started to think about its production, because without production-consumption is impossible. Agriculture is the base of Indian agronomy or rural economy and the proper management of land is most essential for the same. We also study a systematic investigation on the Vedic agricultural system to prove is as the base of modern agronomy. Vedic Mathematics is an ancient system of calculation which was discovered from the Vedas between 1911 and 1918 by Sri Bharati Krishna Tirthaji Maharaj (1884-1960). Vedic Mathematics is a collection of techniques and formulas to solve mathematical arithmetic in easy and faster way; it offers a new and entirely different approach to the study of Vedic Mathematics based on pattern recognition. Mathematics is practical science as it helps us with the daily life. Arithmetic computations cannot be obtained faster by any other known method rather than Vedic mathematics, so this is the best way of understanding mathematics to agriculture students.
This paper concerns with the study of (p, q)-analogue of genuine Baskakov-Durrmeyer type operator... more This paper concerns with the study of (p, q)-analogue of genuine Baskakov-Durrmeyer type operators. We establish the direct approximation theorem, a weighted approximation theorem followed by the estimations of the rate of convergence of these operators for functions of polynomial growth on the interval [)
This paper is the study of two different general linear positive operators defined on unbounded i... more This paper is the study of two different general linear positive operators defined on unbounded interval. Here we introduce a generalized family of the hybrid integral operators. The special cases of our operators include some well known integral operators. The main aim of the present note is to prevent the researchers to study individual operators, and by this form they can study the approximation properties of any linear positive operator by differences of other forms of the same operator. We obtain estimates for the difference of these operators namely Lupas operators in quantitative form. We study quantitative estimates for the difference of generalized Lupas-Szasz and generalized Lupas-Kantorovich operators. Finally, we obtain the quantitative estimate in terms of the weighted modulus of smoothness for these operators. Also, their mutual differences are possible, which are estimated in the present paper. Here, we obtain a new approach to find the moments using the concept of moment generating functions.
World Scientific, 2021
In the year 2003, Srivastava-Gupta proposed a general family of linear positive operators, having... more 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 summationintegral 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.
Springer, 2020
Motivated by recent investigations, in this paper we introduce (p, q)-Szász-beta-Stancu operators... more Motivated by recent investigations, in this paper we introduce (p, q)-Szász-beta-Stancu operators and investigate their local approximation properties in terms of modulus of continuity. We also obtain a weighted approximation and Voronovskaya-type asymptotic formula.
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.
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.
Filomat, 2015
Very recently the modified form of Srivastava-Gupta operators was studied in order to preserve th... more Very recently the modified form of Srivastava-Gupta operators was studied in order to preserve the linear functions. Here, we estimate the rate of approximation for functions having bounded derivatives of the modified form.
gmj, 2006
In this paper we study the modified Beta operators. We extend the result of [Gupta and Ahmad, İst... more In this paper we study the modified Beta operators. We extend the result of [Gupta and Ahmad, İstanbul niv. Fen Fak. Mat. Derg. 54: 11–22 1995] and obtain an inverse result for the linear combination of these modified Beta operators in simultaneous approximation.
Demonstratio Mathematica, 2009
In the year 1993, Gupta and Srivastava [3] introduced the integral modification of the well known... more In the year 1993, Gupta and Srivastava [3] introduced the integral modification of the well known Baskakov operators by taking the weight functions of Szasz basis function, so called Baskakov-Szasz operators. In this paper, we obtain some direct theorems for the linear combination of these Baskakov Szasz type operators. To prove our one of the direct theorems, we use the technique of a mathematical tool which is the linear approximating method and is known as the Steklov means.
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.
International Journal of Mathematics and Mathematical Sciences, 2009
We establish the rate of convergence for the modified Beta operators , for functions having deriv... more We establish the rate of convergence for the modified Beta operators , for functions having derivatives of bounded variation.
International Journal of Mathematics and Mathematical Sciences, 2003
We obtain a converse theorem for the linear combinations of modified beta operators whose weight ... more We obtain a converse theorem for the linear combinations of modified beta operators whose weight function is the Baskakov operators. To prove our inverse theorem, we use the technique of linear approximating method, namely, Steklov mean.
Applied Mathematics E-Notes, 2007
In the present paper we obtain a saturation theorem for the linear combination of modified Beta o... more In the present paper we obtain a saturation theorem for the linear combination of modified Beta operators.
Demonstratio Mathematica, 2015
The applications of q-calculus in the approximation theory is a very interesting area of research... more The applications of q-calculus in the approximation theory is a very interesting area of research in the recent years, several new q-operators were introduced and their behaviour were discussed by many researchers. This paper is the extension of the paper [15], in which Durrmeyer type generalization of q-Baskakov-Stancu type operators were discussed by using the concept of q-integral operators. Here, we propose to study the Stancu variant of q-Baskakov-Stancu type operators. We establish an estimate for the rate of convergence in terms of modulus of continuity and weighted approximation properties of these operators.
Nepal Journal of Mathematical Sciences, 2021
This paper concerns with the study of(p, q)-analogue of genuine Baskakov-Durrmeyer type operators... more This paper concerns with the study of(p, q)-analogue of genuine Baskakov-Durrmeyer type operators. We establish the direct approximation theorem, a weighted approximation theorem followed by the estimations of the rate of convergence of these operators for functions of polynomial growth on the interval [)
Current Overview on Science and Technology Research Vol. 3
In this paper, we show the importance of Vedic mathematics to derive the optimal solution in agri... more In this paper, we show the importance of Vedic mathematics to derive the optimal solution in agriculture e.g. for soil management and crop production, sowing of seeds etc. Since the primary requirement of any being is food i.e. anna, a man started to think about its production, because without production-consumption is impossible. Agriculture is the base of Indian agronomy or rural economy and the proper management of land is most essential for the same. We also study a systematic investigation on the Vedic agricultural system to prove is as the base of modern agronomy. Vedic Mathematics is an ancient system of calculation which was discovered from the Vedas between 1911 and 1918 by Sri Bharati Krishna Tirthaji Maharaj (1884-1960). Vedic Mathematics is a collection of techniques and formulas to solve mathematical arithmetic in easy and faster way; it offers a new and entirely different approach to the study of Vedic Mathematics based on pattern recognition. Mathematics is practical science as it helps us with the daily life. Arithmetic computations cannot be obtained faster by any other known method rather than Vedic mathematics, so this is the best way of understanding mathematics to agriculture students.
This paper concerns with the study of (p, q)-analogue of genuine Baskakov-Durrmeyer type operator... more This paper concerns with the study of (p, q)-analogue of genuine Baskakov-Durrmeyer type operators. We establish the direct approximation theorem, a weighted approximation theorem followed by the estimations of the rate of convergence of these operators for functions of polynomial growth on the interval [)
This paper is the study of two different general linear positive operators defined on unbounded i... more This paper is the study of two different general linear positive operators defined on unbounded interval. Here we introduce a generalized family of the hybrid integral operators. The special cases of our operators include some well known integral operators. The main aim of the present note is to prevent the researchers to study individual operators, and by this form they can study the approximation properties of any linear positive operator by differences of other forms of the same operator. We obtain estimates for the difference of these operators namely Lupas operators in quantitative form. We study quantitative estimates for the difference of generalized Lupas-Szasz and generalized Lupas-Kantorovich operators. Finally, we obtain the quantitative estimate in terms of the weighted modulus of smoothness for these operators. Also, their mutual differences are possible, which are estimated in the present paper. Here, we obtain a new approach to find the moments using the concept of moment generating functions.
World Scientific, 2021
In the year 2003, Srivastava-Gupta proposed a general family of linear positive operators, having... more 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 summationintegral 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.
Springer, 2020
Motivated by recent investigations, in this paper we introduce (p, q)-Szász-beta-Stancu operators... more Motivated by recent investigations, in this paper we introduce (p, q)-Szász-beta-Stancu operators and investigate their local approximation properties in terms of modulus of continuity. We also obtain a weighted approximation and Voronovskaya-type asymptotic formula.
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.