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

@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},
      doi = {https://doi.org/10.64388/IREV9I10-1716749}
  }