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Theory of Certain Non-Univalent Analytic Functions

  • Kamaljeet Gangania
Published/Copyright: October 7, 2023
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 73 Issue 5

ABSTRACT

We investigate the non-univalent function’s properties reminiscent of the theory of univalent starlike functions. Let the analytic function ψ(z)=∑i=1∞Aizi , A1 ≠ 0 be univalent in the unitdisk. Non-univalent functions may be found in the class ℱ(ψ) of analytic functions f of the form f(z)=z+∑k=2∞akzk satisfying (zf′ (z)/f (z) – 1) ≺ ψ(z). Such functions, like the Ma and Minda classes k=2 of starlike functions, also have nice geometric properties. For these functions, growth and distortion theorems have been established. Further, we obtain bounds for some sharp coefficient functionals and establish the Bohr and Rogosinki phenomenon for the class ℱ(ψ) . Non-analytic functions that share properties of analytic functions are known as poly-analytic functions. Moreover, we compute Bohr and Rogosinski’s radius for poly-analytic functions with analytic counterparts in the class ℱ(ψ) or classes of Ma-Minda starlike and convex functions.

2020 Mathematics Subject Classification: Primary 30C45; 30C35; 30C50; Secondary 35Q30
Keywords: Poly-analytic; bi-analytic; non-univalent; starlike; Bohr and Rogosinski’s inequality; coefficient problems

(Communicated by Stanisława Kanas)

Funding statement: The work of Kamajeet Gangania is supported by University Grant Commission, New-Delhi, India under UGC-Ref. No.:1051/(CSIR-UGC NET JUNE 2017).

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Received: 2022-07-06
Accepted: 2022-10-27
Published Online: 2023-10-07

© 2023 Mathematical Institute Slovak Academy of Sciences

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  3. Enlargements of Quantales
  4. Multiplicative Dependent Pairs in the Sequence of Padovan Numbers
  5. Dirichlet Series with Periodic Coefficients, Riemann’s Functional Equation, and Real Zeros of Dirichlet L-Functions
  6. On the Rational Parametric Solution of Diagonal Quartic Varieties
  7. Theory of Certain Non-Univalent Analytic Functions
  8. Initial Coefficients and Fekete-Szegő Inequalities for Functions Related to van der Pol Numbers (VPN)
  9. A Conjecture on H3(1) for Certain Starlike Functions
  10. Coefficient Problems of Quasi-Convex Mappings of Type B on the Unit Ball in Complex Banach Spaces
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  13. On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions
  14. On the Existence of Bi-Lipschitz Equivalent Metrics in Semimetric Spaces
  15. The Lehmann Type II Teissier Distribution
  16. Asymptotic Predictive Inference of Negative Lower Tail Index Distributions
  17. On Numerical Problems in Computing Life Annuities Based on the Makeham–Beard Law
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https://doi.org/10.1515/ms-2023-0086
Keywords for this article
Poly-analytic; bi-analytic; non-univalent; starlike; Bohr and Rogosinski’s inequality; coefficient problems

Articles in the same Issue

  1. Remembering Professor Štefan Znám, 9.2.1936–17.7.1993
  2. Chordal and Perfect Zero-Divisor Graphs of Posets and Applications to Graphs Associated with Algebraic Structures
  3. Enlargements of Quantales
  4. Multiplicative Dependent Pairs in the Sequence of Padovan Numbers
  5. Dirichlet Series with Periodic Coefficients, Riemann’s Functional Equation, and Real Zeros of Dirichlet L-Functions
  6. On the Rational Parametric Solution of Diagonal Quartic Varieties
  7. Theory of Certain Non-Univalent Analytic Functions
  8. Initial Coefficients and Fekete-Szegő Inequalities for Functions Related to van der Pol Numbers (VPN)
  9. A Conjecture on H3(1) for Certain Starlike Functions
  10. Coefficient Problems of Quasi-Convex Mappings of Type B on the Unit Ball in Complex Banach Spaces
  11. Complete Monotonicity and Inequalities Involving the k-Gamma and k-Polygamma Functions
  12. Study of Oscillation Criteria of Odd-Order Differential Equations with Mixed Neutral Terms
  13. On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions
  14. On the Existence of Bi-Lipschitz Equivalent Metrics in Semimetric Spaces
  15. The Lehmann Type II Teissier Distribution
  16. Asymptotic Predictive Inference of Negative Lower Tail Index Distributions
  17. On Numerical Problems in Computing Life Annuities Based on the Makeham–Beard Law
  18. The Rational Zero-Divisor Cup-Length of Oriented Partial Flag Manifolds
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