Some Approximation Properties of Modified Jain-Beta Operators

Abstract

Generalization of Szász-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 parametersα,β, andγand discuss Voronovskaja asymptotic formula.

Approximation Properties of Certain Summation Integral Type Operators

“…Many other researchers work in this direction and obtain different approximation properties of many operators [19,20,15,16,11,1]. Motivated by such type operators, we introduced Stancu type generalization of integral modification of the well known Baskakov operators with the weight function of Beta basis function as:…”

Some approximation properties of a new class of linear operators

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Approximation properties of modified Szász–Mirakyan operators in polynomial weighted space

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