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Hankel determinant for a class of analytic functions involving conical domains defined by subordination

  • Srinivasan Annamalai EMAIL logo , Srikandan Sivasubramanian and Chellakutty Ramachandran
Published/Copyright: July 14, 2017
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 67 Issue 4

Abstract

Domains with conical sections is an underlying concept in the area of complex function theory although is an interesting topic and it deserves more attention. There has been many works focusing towards this area for the past two decades. However, the concept of Hankel determinant has not been studied so far. Exploiting this, we provide an estimate for the Hankel determinant with domains bounded by conical sections. The authors sincerely hope this article will revive and encourage the other researchers to obtain similar sort of estimates for other classes connected with conical domains. The concept of conical domains was introduced by Kanas and Wiśniowska.

MSC 2010: Primary 30C45; 33C50; Secondary 30C80
Keywords: analytic function; univalent function; Hankel determinant; differential subordination and conical region

(Communicated by Stanisława Kanas)

The author would like to thank the referee(s) for their critical comments and the Editor for many insightful suggestions that essentially improved the paper. The second-named is supported by a grant from the Department of Science and Technology of the Government of India (vide ref: SR/FTP/MS-022/2012) under its Young Faculty Fast Track Scheme.

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Received: 2015-5-8
Accepted: 2015-10-7
Published Online: 2017-7-14
Published in Print: 2017-8-28

© 2017 Mathematical Institute Slovak Academy of Sciences

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  4. Hamiltonian ordered algebras and congruence extension
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  8. Only finitely many Tribonacci Diophantine triples exist
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  16. M-Cantorvals of Ferens type
  18. Comparison of ψ-porous topologies
  20. On certain generalized matrix methods of convergence in (ℓ)-groups
  22. Some applications of first-order differential subordinations
  24. Hankel determinant for a class of analytic functions involving conical domains defined by subordination
  26. Nonoscillation and exponential stability of the second order delay differential equation with damping
  28. Positive solutions of perturbed nonlinear hammerstein integral equation
  30. Ricci solitons on 3-dimensional cosymplectic manifolds
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https://doi.org/10.1515/ms-2017-0023
Keywords for this article
analytic function; univalent function; Hankel determinant; differential subordination and conical region

Articles in the same Issue

  2. Outer measure on effect algebras
  4. Hamiltonian ordered algebras and congruence extension
  6. Automorphism groups with some finiteness conditions
  8. Only finitely many Tribonacci Diophantine triples exist
  10. Abundant semigroups with a *-normal idempotent
  12. Stability results for fractional differential equations with state-dependent delay and not instantaneous impulses
  14. Monotonicity results for delta fractional differences revisited
  16. M-Cantorvals of Ferens type
  18. Comparison of ψ-porous topologies
  20. On certain generalized matrix methods of convergence in (ℓ)-groups
  22. Some applications of first-order differential subordinations
  24. Hankel determinant for a class of analytic functions involving conical domains defined by subordination
  26. Nonoscillation and exponential stability of the second order delay differential equation with damping
  28. Positive solutions of perturbed nonlinear hammerstein integral equation
  30. Ricci solitons on 3-dimensional cosymplectic manifolds
  32. Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups
  34. The super socle of the ring of continuous functions
  36. On the internal approach to differential equations 2. The controllability structure
  38. Finiteness of the discrete spectrum in a three-body system with point interaction
  40. On a subclass of Bazilevic functions
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