The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*
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Shagun Banga
Abstract
In this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Carathéodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H3(1) and H2(3) for the well known class 𝓢𝓛* of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional:
The first author is supported by a Research Fellowship from the Department of Science and Technology, New Delhi (Ref No. IF170272). The work of second author is supported by the Faculty Research Project grant of DTU (Ref No. DTU/Council/BOM-AC/Notification/31/2018/5738)
(Communicated by Stanisława Kanas)
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© 2020 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular papers
- Some relative normality properties in locales
- Upper bounds of some special zeros for the Rankin-Selberg L-function
- Factorization of polynomials over valued fields based on graded polynomials
- Varieties of ∗-regular rings
- On reverse Hölder and Minkowski inequalities
- Coefficient inequalities related with typically real functions
- Existence of wandering and periodic domain in given angular region
- The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*
- Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space
- Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces
- Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces
- 𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms
- More on closed non-vanishing ideals in CB(X)
- The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data
- Multi-opponent James functions
- An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications
- A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models
- On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation
- Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations
Articles in the same Issue
- Regular papers
- Some relative normality properties in locales
- Upper bounds of some special zeros for the Rankin-Selberg L-function
- Factorization of polynomials over valued fields based on graded polynomials
- Varieties of ∗-regular rings
- On reverse Hölder and Minkowski inequalities
- Coefficient inequalities related with typically real functions
- Existence of wandering and periodic domain in given angular region
- The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*
- Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space
- Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces
- Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces
- 𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms
- More on closed non-vanishing ideals in CB(X)
- The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data
- Multi-opponent James functions
- An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications
- A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models
- On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation
- Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations
