Zalcmann, Generalized Zalcmann and Krushkal inequalities associated with a new subclass of analytic functions

  • Vishnu M Vishnu Mohanan Marar Vidyavardhaka College of Engineering
  • M. Nandeesh
  • M. Ruby Salestina

Resumo

In this article we investigate the sharp bounds of Zalcmann, generalized Zalcmann and Krushkal inequalities for a new subclass of analytic functions of the form $ f(z)=z +\sum_{n=2}^{\infty} a_n z^n$ on the unit disk $\Delta=\{z \in
\mathbb{C}: |z|<1\}.$

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Referências

J.E. Brown, A. Tsao., On the Zalcman conjecture for starlike and typically real functions, Math. Z., 191 (3), (1986), 467–474.

P. L. Duren.,Univalent functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, (1983).

S. L. Krushkal.,Proof of the Zalcman conjecture for initial coefficients, Georgian Math. J., (2010), vol. 17, pp. 663–681

S. L. Krushkal.,A short geometric proof of the Zalcman and Bieberbach conjectures, (2014)

L. Li, S. Ponnusamy, On the generalized Zalcman functional in the close-to-convex family, Proc. Amer. Math. Soc., 145,(2017), 833–846

L. Li, S. Ponnusamy, J. Qiao., Generalized Zalcman conjecture for convex functions of order α, Acta Math. Hungar. 150 (1), (2016), 234–246

W.C. Ma.,Generalized Zalcman conjecture for star - like and typically real functions, J. Math. Anal. Appl, (1999), Volume 234(1), 328 - 339

W.C. Ma.,The Zalcman conjecture for close-to-convex functions, Proc. Amer. Math. Soc., 104 (3), (1988), 741–744

S. Ozaki, M. Nunokawa., The Schwarzian derivative and univalent functions, Proc. Amer. Math. Soc, (1972), Volume 33(2), 392 - 394

V. Ravichandran, S. Verma,Generalized Zalcman conjecture for some classes of analytic functions, J. Math. Anal. Appl, (2017), Volume 450(1), 592 - 605

D. K. Thomas, N. Tuneski, A. Vasudevarao.,Univalent functions, A primer, De Gruyter Studies in Mathematics, De Gruyter, Berlin, (2018)

Publicado
2025-08-10
Seção
Artigos