The Complex Form of a New Generalization of the Bernstein Operator, Depending On a Non-Negative Real Parameter

• Author(s): Amish Kumar; Shivani Sharma; Dipika Gautam; Chandra Mukesh Swami
• Paper ID: 1716749
• Page: 3302-3331
• Published Date: 30-04-2026
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 9 Issue 10 April-2026
• DOI: https://doi.org/10.64388/IREV9I10-1716749

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, vol. 9, no. 10, Apr. 2026, doi: https://doi.org/10.64388/IREV9I10-1716749

APA:
Amish Kumar, Shivani Sharma, Dipika Gautam, Chandra Mukesh Swami (2026). 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). doi: https://doi.org/10.64388/IREV9I10-1716749

MLA:
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, vol. 9, no. 10, Apr. 2026. Crossref, https://doi.org/10.64388/IREV9I10-1716749

BibTeX

@article{1716749,
author = {Amish Kumar, Shivani Sharma, Dipika Gautam, Chandra Mukesh Swami},
title = {The Complex Form of a New Generalization of the Bernstein Operator, Depending On a Non-Negative Real Parameter},
journal = {Iconic Research And Engineering Journals},
year = {2026},
volume = {9},
number = {10},
pages = {3302-3331},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1716749.pdf},
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.},
month = {April}
}