Simultaneous Approximation for Beta-Baskakov-Stancu Operators (original) (raw)
Some Approximation Properties of -Baskakov-Beta-Stancu Type Operators
Journal of Calculus of Variations, 2013
This paper deals with new typeq-Baskakov-Beta-Stancu operators defined in the paper. First, we have used the properties ofq-integral to establish the moments of these operators. We also obtain some approximation properties and asymptotic formulae for these operators. In the end we have also presented better error estimations for theq-operators.
Direct Theorems for Modified Baskakov Stancu Operators in Simultaneous Approximation
Global Journal of Pure and Applied Mathematics, 2015
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.
On approximation properties of Baskakov–Szász–Stancu operators using hypergeometric representation
Applied Mathematics and Computation, 2017
In the present paper, we study the mixed summation integral type operators having Baskakov and Szász basis functions in summation and integration form, respectively. We also give here the alternate form of the operators in terms of hypergeometric functions and estimated moments of these operators using hypergeometric series. In the last section, we present some results for operators related to convergence.
SOME APPROXIMATION PROPERTIES OF MODIFIED BASKAKOV STANCU OPERATORS
In the present paper, we prove a global direct theorem for the modified Baskakovstancu operators in terms of Ditzian-Totik modulus of smoothness. Here, we have modified our operators by taking weight function of Beta operators and then generalizing it as stancu type generalized operators. We will also see that taking weight function of Beta operators will give better approximation. We study a global direct theorem using simultaneous approximation for ourstancu type generalized operator in í µí°¿ í µí± 0, ∞. Here, first we estimate recurrence relation for moments and then develop some global direct results by making our stancu type generalized operators positive using differential and integral operators. In this paper, our effort is to give better global approximation for our stancu type generalized operator than the earlier integral modifications of Baskakov operators studied by various authors. Here, we will extend our results for the whole interval 0, ∞. In this paper, we will also make use of the fact that second modulus of smoothness introduced by Ditzian-Totik is equivalent to modified k-functional and í µí°¿ í µí± í µí± [0, ∞) is not contained in í µí°¿ 1 í µí± [0, ∞) for obtaining results. Here, Riesz-Thorin theorem and Leibnitz theorem is used extensively for doing simultaneous approximation. We have also used Fubini's theorem for obtaining results.
Hypergeometric Representation for Baskakov-Durrmeyer-Stancu Type Operators
2013
In the present paper, we introduce and study the mixed summationintegral type operators having Baskakov and Beta basis functions in summation and integration, respectively. First, we estimate moments of these operators using hypergeometric series. Next, we obtain an error estimation in simultaneous approximation for Baskakov-Durrmeyer-Stancu operators. 0 2000 Mathematics Subject Classification: 41A25, 41A35.
Simultaneous approximation by certain Baskakov–Durrmeyer–Stancu operators
In the present paper, we establish some direct results in simultaneous approximation for Baskakov-Durrmeyer-Stancu (abbr. BDS) operators D ða;bÞ n ðf; xÞ. We establish point-wise convergence, Voronovskaja type asymptotic formula and an error estimate in terms of second order modulus of continuity of the function.
2013
Khan [4] and Mishra [5] have proved some results dealing with the degree of approximation of functions in Lpspaces using different types of operators. BaskakovDurrmeyer operators were first considered by Sahai-Prasad [8] in 1985 . Sinha et al. [9] improved and corrected the results of [8]. In 2005, Finta [1], introduced a new type of Baskakov-Durrmeyer operator by taking the weight function of Beta operators on L[0,∞) as
Approximation Properties by Generalized-Baskakov- Kantorovich-Stancu Type Operators
Applied Mathematics & Information Sciences Letters, 2016
In this paper, we introduce generalized Baskakov Kantorovich Stancu type operators and investigate direct result, local approximation and weighted approximation properties of these operators. Modulus of continuity, second modulus of continuity, Peeter's K-functional, weighted modulus of continuity and Lipschitz class are considered to prove our results.
On Simultaneous Approximation for Certain Baskakov Durrmeyer Type Operators
Journal of Inequalities in Pure and Applied Mathematics, 2006
In the present paper, we study a certain integral modification of the well known Baskakov operators with the weight function of Beta basis function. We establish pointwise convergence, an asymptotic formula an error estimation and an inverse result in simultaneous approximation for these new operators.
Approximation by Jakimovski-Leviatan-Stancu-Durrmeyer type operators
Filomat, 2019
In the present paper, we introduce Stancu type modification of Jakimovski-Leviatan-Durrmeyer operators. First, we estimate moments of these operators. Next, we study the problem of simultaneous approximation by these operators. An upper bound for the approximation to rth derivative of a function by these operators is established. Furthermore, we obtain A-statistical approximation properties of these operators with the help of universal korovkin type statistical approximation theorem.
Stancu-variant of generalized Baskakov operators
In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.
On generalized Baskakov-Durrmeyer-Stancu type operators
Demonstratio Mathematica
In this paper, we study some local approximation properties of generalized Baskakov-Durrmeyer-Stancu operators. First, we establish a recurrence relation for the central moments of these operators, then we obtain a local direct result in terms of the second order modulus of smoothness. Further, we study the rate of convergence in Lipschitz type space and the weighted approximation properties in terms of the modulus of continuity, respectively. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.
Stancu Type Baskakov—Durrmeyer Operators and Approximation Properties
Mathematics, 2020
In this article, we introduce Stancu type generalization of Baskakov–Durrmeyer operators by using inverse Pólya–Eggenberger distribution. We discuss some basic results and approximation properties. Moreover, we study the statistical convergence for these operators.
Mathematics
The goal of this research article is to introduce a sequence of α–Stancu–Schurer–Kantorovich operators. We calculate moments and central moments and find the order of approximation with the aid of modulus of continuity. A Voronovskaja-type approximation result is also proven. Next, error analysis and convergence of the operators for certain functions are presented numerically and graphically. Furthermore, two-dimensional α–Stancu–Schurer–Kantorovich operators are constructed and their rate of convergence, graphical representation of approximation and numerical error estimates are presented.
Approximation on a class of Szász–Mirakyan operators via second kind of beta operators
Journal of Inequalities and Applications
In the present article, we construct a new sequence of positive linear operators via Dunkl analogue of modified Szász–Durrmeyer operators. We study the moments and basic results. Further, we investigate the pointwise approximation and uniform approximation results in various functional spaces for these sequences of positive linear operators. Finally, we prove the global approximation and A-statistical convergence results for these operators.
Some approximation properties by q-Szász-Mirakyan-Baskakov-Stancu operators
In the present paper we propose the Stancu type generalization of q-Sz´asz-Mirakyan-Baskakov operators (see e.g. ). We apply q-derivatives, and q-Beta functions to obtain the moments of the q-Sz´asz-Mirakyan-Baskakov-Stancu operators. Here we estimate some direct approximation results for these operators.
On Stancu type generalization of -Baskakov operators
Mathematical and Computer Modelling, 2010
In this paper, we consider a generalization of q-Baskakov operators. We obtain local approximation theorem on the interval [0, ∞) and also obtain rate of convergence for these new operators in the weighted space.
ASYMPTOTIC FORMULA FOR MODIFIED BETA OPERATORS
For last three decades applications of beta operators in the area of approximation theory is an active area of research. In the present paper, we obtain asymptotic formula for modified beta operators in linear simultaneous approximation. To establish our result, we have used the technique of linear approximating method, namely, Steklov mean.
Approximation Properties of Modified Baskakov Gamma Operators
Facta Universitatis, Series: Mathematics and Informatics, 2021
In this present paper, we study an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem we first give approximation properties of this operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we give an approximation properties of weighted spaces. Finally, we study the Voronovskaya type theorem of this operator.