Coefficient Estimates and Geometric Analysis of a New Bi-Univalent Function Class


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Authors

  • Debasmita Dash Department of Mathematics, O. P. Jindal University, Raigarh, Chhattisgarh, India
  • Saumya Singh Department of Mathematics, O. P. Jindal University, Raigarh, Chhattisgarh, India
  • Abhishek Kumar Singh Department of Mathematics, United College of Engineering and Research, Prayagraj, Uttar Pradesh, India
  • Debasmita Samal Department of Mathematics, O. P. Jindal University, Raigarh, Chhattisgarh, India
  • Manas Ranjan Mishra Department of Mathematics, O. P. Jindal University, Raigarh, Chhattisgarh, India
  • Swati ­Verma Department of Mathematics, O. P. Jindal University, Raigarh, Chhattisgarh, India

Keywords:

Analytic Functions, Bi-univalent Functions, Generalized Sălăgean operator, Argument condition, Subordination, Coefficient bounds

Abstract

In this research, we establish two recently formulated subclasses belonging to the bi-univalent analytic functions characterized by the generalized Sălăgean operator The first subclass  consisting of bi-univalent functions within the unit disk  and its extended form of subclass  are defined by specific argument conditions involving parameters  and . Using the concept of subordination and functions with positive real part, the initial coefficients  and  are estimated with established limits. The results generalize and unify several existing analytic and bi-univalent function’s subclasses. Special cases are discussed to demonstrate the significance and sharpness of the obtained estimates. Additionally, we also analyse the geometric behaviour of functions under this new operator.   

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Published

2026-01-28

How to Cite

Debasmita Dash, Saumya Singh, Abhishek Kumar Singh, Debasmita Samal, Manas Ranjan Mishra, & Swati ­Verma. (2026). Coefficient Estimates and Geometric Analysis of a New Bi-Univalent Function Class. Results in Nonlinear Analysis, 8(4), 35–43. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/773

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Vol. 8 No. 4 (2025): Online First

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