ON CERTAIN GENERALIZED MODIFIED BETA OPERATORS (original) (raw)

© Impact Journals ON CERTAIN GENERALIZED MODIFIED BETA OPERATORS

IMPACT , 2015

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.

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.

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.

ON A GENERAL CLASS OF BETA APPROXIMATING OPERATORS OF SECOND KIND

We shall define a general linear transform, from which we obtain as special case the beta second kind transform. We obtain several positive linear operators as a special case of this beta second kind transform. We apply the beta second kind transform to Baskakov's operator Bn and we obtain different generalization of it.

On the Modified Beta Approximating Operators of First Kind

2004

We define a general linear operator from which we obtain as special case the modified beta first kind operator (Bp,qf)(x) = 1 B(p,q) 1 0 t p−1 (1 − t) q−1 f B(p,q) B(p+a,q) t a x dt. We consider here only the cases a = 1 and a = −1. We obtain several positive linear operators as particular cases of this modified beta first kind operator. MSC 2000. 41A36. Keywords. Euler's beta function, the modified beta first kind operator, positive linear operators.

Asymptotic Approximation with Stancu Beta Operators

1998

The concern of this paper is a beta type operator Ln recently introduced by D. D. Stancu. We present the complete asymptotic expansion for Ln as n tends to infinity. All coefficients of n −k (k = 1, 2,. . .) are calculated explicitly in terms of Stirling numbers of the first and second kind. Moreover, we give an asymptotic expansion for Ln into a series of reciprocal factorials. MSC 2000. 41A36.

Statistical approximation properties of modified q-Stancu-Beta operators

Abstract. In this paper we define the modified q-Stancu-Beta operators and study the weighted statistical approximation by these operators with the help of the Korovkin type approximation theorem. We also establish the rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function. Our results show that rates of convergence of our operators are at least as fast as classical Stancu-Beta operators.

The Beta Approximating Operators of First Kind

We shall define a general linear transform from which we obtain as particular case the beta first kind transform: Bp,qf = 1 B(p, q) 1 0 t p−1 (1 − t) q−1 f (t a)dt (*) We consider here only the particular case a = 1. We obtain several positive linear operators as a particular case of this beta first kind transform. We apply the transform (*) to Bernstein's operator Bn and thus we obtain different generalizations of this operator.