Gregory Polynomials Within Sakaguchi-Type Function Classes: Analytical Estimates and Geometric Behavior

Akgül A., Oros G. I.

SYMMETRY-BASEL, cilt.17, sa.6, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 6
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/sym17060884
  • Dergi Adı: SYMMETRY-BASEL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Kocaeli Üniversitesi Adresli: Evet

Özet

This work introduces a novel family of analytic and univalent functions formulated through the integration of Gregory coefficients and Sakaguchi-type functions. Employing subordination techniques, we obtain sharp bounds for the initial coefficients in their Taylor expansions. The influence of parameter variations is examined through comprehensive geometric visualizations, which confirm the non-emptiness of the class and provide insights into its structural properties. Furthermore, Fekete-Szeg & ouml; inequalities are established, enriching the theory of bi-univalent functions. The combination of analytical methods and geometric representations offers a versatile framework for future research in geometric function theory.