Current Volume 9
The Complex Form of a New Generalization of the Bernstein Operator, Depending On a Non-Negative Real Parameter
Abstract
In this chapter we discuss the complex form of a new generalization of the Bernstein operator, depending on a non-negative real parameter. In which we obtained quantitative upper estimate for simultaneous approximation. In this chapter, we discussed the complex form of a new generalization of the Bernstein operator, depending on a non-negative real parameter and obtained quantitative upper estimate for simultaneous approximation, a qualitative Voronovskaja type result and the exact order of approximation. Also, we present some shape preserving properties of the complex _-Bernstein operator such as univalence, starlikeness, convexity and spirallikeness. We obtained quantitative upper estimate for simultaneous approximation, a qualitative Voronovskaja type result and the exact order of approximation.
Citations
IRE Journals:
Amish Kumar, Shivani Sharma, Dipika Gautam, Chandra Mukesh Swami "The Complex Form of a New Generalization of the Bernstein Operator, Depending On a Non-Negative Real Parameter" Iconic Research And Engineering Journals Volume 9 Issue 10 2026 Page 3302-3331 https://doi.org/10.64388/IREV9I10-1716749
IEEE:
Amish Kumar, Shivani Sharma, Dipika Gautam, Chandra Mukesh Swami
"The Complex Form of a New Generalization of the Bernstein Operator, Depending On a Non-Negative Real Parameter" Iconic Research And Engineering Journals, 9(10) https://doi.org/10.64388/IREV9I10-1716749
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