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Pointwise and weighted estimates for Bernstein-Kantorovich type operators including beta function

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We establish a Kantorovich variant of Bernstein operators including the beta function inspired by the King-type operators which preserve certain functions. We provide some pointwise, weighted, and direct approximation theorems to examine the approximation properties of the introduced sequence of operators. Furthermore, by graphical and numerical examples, we demonstrate the convergence of defined operators with the help of the MATLAB program.

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The first author extends his appreciation to the Deanship of Scientific Research at King Khalid University for funding his work through the research groups program under Grant number RGP. 2/371/44.

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Correspondence to Khursheed J. Ansari.

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Communicated by NM Bujurke.

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Ansari, K.J., Özger, F. Pointwise and weighted estimates for Bernstein-Kantorovich type operators including beta function. Indian J Pure Appl Math (2024).

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