New Results about Radius of Convexity and Uniform Convexity of Bessel Functions

Cotîrlǎ, Luminiţa-Ioana; Kupán, Pál Aurel; Szász, Róbert

doi:10.3390/axioms11080380

Cited by 4 publications

(4 citation statements)

References 12 publications

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“…New results on the radius of uniform convexity of two kinds of normalization of the Bessel function J ν in the case of ν ∈ (−2, −1) are presented by Luminiţa-Ioana Cotîrlă, Pál Aurel Kupán, and Róbert Szász in reference [9]. This study provides alternative proof regarding the radius of convexity of order alpha.…”

Section: Overview Of the Published Papersmentioning

confidence: 86%

New Developments in Geometric Function Theory

Oros

2023

Axioms

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Section: Overview Of the Published Papersmentioning

confidence: 86%

New Developments in Geometric Function Theory

Oros

2023

Axioms

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“…For α + β = 1, γ ≥ 0, Theorem 2 gives the following corollary for Bernardi integral operator given by (15). Corollary 4.…”

Section: A New Generalized Integral Operator Involving Bessel Functio...mentioning

confidence: 97%

“…The present investigation on the Bessel function of the first kind was inspired by the known geometric properties of this function initially established by Á. and further investigated in more recent works like [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Study on the Criteria for Starlikeness in Integral Operators Involving Bessel Functions

Oros,

Bardac-Vlada

2023

Symmetry

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The study presented in this paper follows a line of research familiar for Geometric Function Theory, which consists in defining new integral operators and conducting studies for revealing certain geometric properties of those integral operators such as univalence, starlikness, or convexity. The present research focuses on the Bessel function of the first kind and order ν unveiling the conditions for this function to be univalent and further using its univalent form in order to define a new integral operator on the space of holomorphic functions. For particular values of the parameters implicated in the definition of the new integral operator involving the Bessel function of the first kind, the well-known Alexander, Libera, and Bernardi integral operators can be obtained. In the first part of the study, necessary and sufficient conditions are obtained for the Bessel function of the first kind and order ν to be a starlike function or starlike of order α∈[0,1). The renowned prolific method of differential subordination due to Sanford S. Miller and Petru T. Mocanu is employed in the reasoning. In the second part of the study, the outcome of the first part is applied in order to introduce the new integral operator involving the form of the Bessel function of the first kind, which is starlike. Further investigations disclose the necessary and sufficient conditions for this new integral operator to be starlike or starlike of order 12.

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“…In particular, we aim to focus on the geometrical properties such as radius results related to a class of strongly starlike functions associated with the function ϕ(ζ) = (1 + ζ) λ , 0 < λ < 1 and to build its connection with the renowned classes C, S * η , S * M ,,−US * ,,−UC and S * L of analytic functions, which is the main motivation of this work. For more relevant work, one can see [20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Radius Results for Certain Strongly Starlike Functions

Saliu

Jabeen²,

Xin

et al. 2023

Symmetry

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This article comprises the study of strongly starlike functions which are defined by using the concept of subordination. The function φ defined by φ(ζ)=(1+ζ)λ, 0<λ<1 maps the open unit disk in the complex plane to a domain symmetric with respect to the real axis in the right-half plane. Using this mapping, we obtain some radius results for a family of starlike functions. It is worth noting that all the presented results are sharp.

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New Results about Radius of Convexity and Uniform Convexity of Bessel Functions

Cited by 4 publications

References 12 publications

New Developments in Geometric Function Theory

New Developments in Geometric Function Theory

Study on the Criteria for Starlikeness in Integral Operators Involving Bessel Functions

Radius Results for Certain Strongly Starlike Functions

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