Approximation By 𝒒−Szász-Kantorovich-Chlodowsky Operators On Weighted Spaces

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The main purpose of this research is to apply 𝑞-calculus to some linear positive operators and to estimate the approximation properties of these operators, which is a popular area of study in recent years of the approximation theory which has a significant contribution to mathematics in the last two centuries and has many applications. Firstly some definitions and notations related to 𝑞-calculus are given, then the images of the test functions 1,𝑡,𝑡^2,𝑡^3,𝑡^4 under 𝑞-Szász-Kantorovich-Chlodowsky operators are calculated and the central moments of the 𝑞 -Szász-Kantorovich-Chlodowsky operators up to 4-th order are given. In addition, theorems related to the uniform convergence of the above operator in the weighted spaces and to obtain the degree of approximation of this operator the proof of the Voronovskaja type asymptotic theorem are given. Finally, the rate of convergence in weighted spaces is calculated with the help of modulus of continuity.

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Voronovskaja Type Asymptotic Theorem , Modulus of Continuity , 𝑞 , Szász Mirakyan Operators , Weighted Approximation

Erciyes University Journal Of The Institute Of Science an‎d Technology

149

Erciyes University Journal Of The Institute Of Science an‎d Technology