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Subordination-implication problems concerning the nephroid starlikeness of analytic functions

  • Anbhu Swaminathan EMAIL logo and Lateef Ahmad Wani
Published/Copyright: October 16, 2022
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 72 Issue 5

Abstract

Let A be the set of all analytic functions f defined on the open unit disk D satisfying f(0) = f'(0) − 1 = 0. Let φNe(z) := 1 + z − z3=3 be the recently introduced Carathéodory function which maps the unit circle ∂ D D onto a 2-cusped kidney-shaped curve called nephroid given by ((u−1)2+v2−4a)3−4v22=0. In this paper, we determine the best possible estimate on the real β so that for some analytic p satisfying p(0) = 1 the following subordination-implication holds:

1+βzp′(z)pj(z)≺F(z)⇒p(z)≺φNe(z), j=0,1,2,

where F(z) is some Carathéodory function with special geometries like right/left-half of Bernoulliφs lemniscate, cardioid, lune, eight-shaped, etc. As applications, we establish sufficient conditions for the Ma-Minda family of nephroid starlike functions given by

SNe*:={ f∈A:zf′(z)f(z)≺φNe(z) }.
Keywords: Carathéodory function; differential subordination; starlike function; lemniscate of Bernoulli; cardioid; nephroid
MSC 2010: Primary 30C45; 30C80

This work was supported by the Project No. CRG/2019/000200/MS of Science and Engineering Research Board (SERB), Department of Science and Technology (DST), New Delhi, India.

Acknowledgement

The authors would like to express their gratitude to the anonymous referees for their thoughtful comments and efforts towards improving the paper.

  1. (Communicated by Stanisława Kanas)

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Received: 2021-04-13
Accepted: 2021-09-11
Published Online: 2022-10-16
Published in Print: 2022-10-26

© 2022 Mathematical Institute Slovak Academy of Sciences

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  2. Generalized hyperharmonic number sums with reciprocal binomial coefficients
  3. Gini index on generalized r-partitions
  4. Multiplicative functions of special type on Piatetski-Shapiro sequences
  5. Strengthenings of Young-type inequalities and the arithmetic geometric mean inequality
  6. Generalizations of the steffensen integral inequality for pseudo-integrals
  7. Subordination-implication problems concerning the nephroid starlikeness of analytic functions
  8. Boundedness and almost periodicity of solutions of linear differential systems
  9. On variational approaches for fractional differential equations
  10. Approximity of asymmetric metric spaces
  11. Approximation theorems for the new construction of Balázs operators and its applications
  12. On η-biharmonic hypersurfaces in pseudo-Riemannian space forms
  13. Chen’s first inequality for hemi-slant warped products in nearly trans-Sasakian manifolds
  14. Induced mappings on symmetric products of Hausdorff spaces
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  18. On two correlated linear models with common and different parameters
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https://doi.org/10.1515/ms-2022-0081
Keywords for this article
Carathéodory function; differential subordination; starlike function; lemniscate of Bernoulli; cardioid; nephroid

Articles in the same Issue

  1. Regular Papers
  2. Generalized hyperharmonic number sums with reciprocal binomial coefficients
  3. Gini index on generalized r-partitions
  4. Multiplicative functions of special type on Piatetski-Shapiro sequences
  5. Strengthenings of Young-type inequalities and the arithmetic geometric mean inequality
  6. Generalizations of the steffensen integral inequality for pseudo-integrals
  7. Subordination-implication problems concerning the nephroid starlikeness of analytic functions
  8. Boundedness and almost periodicity of solutions of linear differential systems
  9. On variational approaches for fractional differential equations
  10. Approximity of asymmetric metric spaces
  11. Approximation theorems for the new construction of Balázs operators and its applications
  12. On η-biharmonic hypersurfaces in pseudo-Riemannian space forms
  13. Chen’s first inequality for hemi-slant warped products in nearly trans-Sasakian manifolds
  14. Induced mappings on symmetric products of Hausdorff spaces
  15. The Teissier-G family of distributions: Properties and applications
  16. A new extension of the beta generator of distributions
  17. A new family of compound exponentiated logarithmic distributions with applications to lifetime data
  18. On two correlated linear models with common and different parameters
  19. On some applications of Duhamel operators
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