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Coefficients problems for families of holomorphic functions related to hyperbola

  • Stanisława Kanas EMAIL logo , Vali Soltani Masih and Ali Ebadian
Published/Copyright: May 23, 2020
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 70 Issue 3

Abstract

We consider a family of analytic and normalized functions that are related to the domains ℍ(s), with a right branch of a hyperbolas H(s) as a boundary. The hyperbola H(s) is given by the relation 1ρ=2cos⁡φss(0<s≤1,|φ|<(πs)/2). We mainly study a coefficient problem of the families of functions for which zf′/f or 1 + zf″/f′ map the unit disk onto a subset of ℍ(s) . We find coefficients bounds, solve Fekete-Szegö problem and estimate the Hankel determinant.

Keywords: univalent functions; subordination; starlike and convex functions; domain related to hyperbola; conic sections
MSC 2010: Primary30C45; 30C80

  1. Communicated by Tomasz Natkaniec

Acknowledgement

The authors thank the editor and the anonymous referees for constructive and pertinent suggestions.

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Received: 2019-04-02
Accepted: 2019-09-21
Published Online: 2020-05-23
Published in Print: 2020-06-25

© 2020 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0375
Keywords for this article
univalent functions; subordination; starlike and convex functions; domain related to hyperbola; conic sections

Articles in the same Issue

  1. Regular papers
  2. Recurrences for the genus polynomials of linear sequences of graphs
  3. The existence of states on EQ-algebras
  4. On sidon sequences of farey sequences, square roots and reciprocals
  5. Repdigits as sums of three balancing numbers
  6. Lipschitz one sets modulo sets of measure zero
  7. Refinement of fejér inequality for convex and co-ordinated convex functions
  8. An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials
  9. Coefficients problems for families of holomorphic functions related to hyperbola
  10. Triebel-Lizorkin capacity and hausdorff measure in metric spaces
  11. The method of upper and lower solutions for integral boundary value problem of semilinear fractional differential equations with non-instantaneous impulses
  12. On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers
  13. Density of summable subsequences of a sequence and its applications
  14. Rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space
  15. A note on cosine series with coefficients of generalized bounded variation
  16. Some geometric properties of the non-Newtonian sequence spaces lp(N)
  17. On sequence spaces defined by the domain of a regular tribonacci matrix
  18. Jointly separating maps between vector-valued function spaces
  19. Some fixed point theorems for multi-valued mappings in graphical metric spaces
  20. Monotone transformations on the cone of all positive semidefinite real matrices
  21. Locally defined operators in the space of Ck,ω-functions
  22. Some properties of D-weak operator topology
  23. Estimating the distribution of a stochastic sum of IID random variables
  24. An internal characterization of complete regularity
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