Starting from a sequence of linear positive operators introduced by G.C. Jain, we present an integral version of it. Approx- imation properties and the rate of convergence are investigated. We use the concept of A-statistical convergence. An extension for smooth functions is also given.

/pdf/on-jain-beta-linear-operators-3zgd6ytcob.pdf

On Jain-Beta Linear Operators

Generalization of Szasz-Mirakyan operators has been considered by Jain, 1972. Using these generalized operators, we introduce new sequences of positive linear operators which are the integral modification of the Jain operators having weight functions of some Beta basis function. Approximation properties, the rate of convergence, weighted approximation theorem, and better approximation are investigated for these new operators. At the end, we generalize Jain-Beta operator with three parameters , , and and discuss Voronovskaja asymptotic formula.

/pdf/some-approximation-properties-of-modified-jain-beta-2fb5uhtbfy.pdf

Some Approximation Properties of Modified Jain-Beta Operators

By using given arbitrary sequences,property that limn 1nn= 0and limn 1 n= 0, we give a Kantorovichtype generalization of Jain operator based on the a Poisson disrtibition. Fristlywe give the quantitative Voronovskaya type theorem. Then we also obtain theGruss Voronovskaya type theorem in quantitative form .We show that theyhave an arbitrary good order of weighted approximation

/pdf/quantitative-estimates-for-jain-kantorovich-operators-1lvt4hf8cy.pdf

Quantitative estimates for Jain-Kantorovich operators

The topic of the present paper are certain approximation operators acting on the space of continous functions on [0,+?) having polynomial growth. The operators which were defined by Jain in 1972 are based on a probability distribution which is called generalized Poisson distribution. As a main result we derive a complete asymptotic expansion for the sequence of these operators.

Asymptotic behaviour of Jain operators

In the present paper, we discuss the approximation properties of Durrmeyer-Stancu type variant of Jain operators with the modified forms of the Beta basis functions. We establish some direc...

The Integral Type Modification of Jain Operators and its Approximation Properties

http://dergiler.ankara.edu.tr/dergiler/29/1252/14348.pdf

Approximation of function by a generalized szars operators

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Approximation of function by a generalized szars operators