The radius of convexity of normalized Bessel functions
TLDR
In this article, the radius of convexity of two normalized Bessel functions of the first kind was determined in the case when the order is between $-2$ and $-1.$.Abstract:
The radius of convexity of two normalized Bessel functions of the first kind are determined in the case when the order is between $-2$ and $-1.$ Our methods include the minimum principle for harmonic functions, the Hadamard factorization of some Dini functions, properties of the zeros of Dini functions via Lommel polynomials and some inequalities for complex and real numbers.read more
Citations
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Journal ArticleDOI
The radius of $\alpha$-convexity of normalized Bessel functions of the first kind
TL;DR: In this article, the radii of starlikeness and convexity for normalized Bessel functions of the first kind were shown to decrease with respect to the parameter of the Bessel function.
Journal ArticleDOI
Geometric properties of some Lommel and Struve functions
TL;DR: In this paper, the authors deduce some new results on the zeros of the derivatives of some Lommel and Struve functions of the first kind and apply these results in order to determine the radii of convexity of some normalized Lommel-Struve functions.
Journal ArticleDOI
Radii of starlikeness and convexity of some q-Bessel functions
TL;DR: In this article, the geometric properties of the Jackson and Hahn-Exton q-Bessel functions are studied and three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane.
Journal ArticleDOI
The Radius of \(\alpha \)-Convexity of Normalized Bessel Functions of the First Kind
TL;DR: In this article, the radii of convexity of normalized Bessel functions of the first kind were shown to decrease with respect to the parameter of the Bessel function, and these radii are between those of star-likeness and convexities.
Journal ArticleDOI
Bounds for Radii of Starlikeness of Some $${\varvec{q}}$$ q -Bessel Functions
TL;DR: In this article, the radii of starlikeness of Jackson's second and third q-Bessel functions are considered and for each of them three different normalization is applied, by applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds are obtained.
References
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Book
Generalized Bessel Functions of the First Kind
TL;DR: In this paper, the generalized Bessel function is defined and a brief outline of Bessel functions is given, including recursive formulas, differentiation formulas, integral representations, and classical inequalities, which will be used in the sequel.
Book ChapterDOI
Geometric Properties of Generalized Bessel Functions
TL;DR: In this article, the authors studied the geometric properties of generalized Bessel functions of the first kind, including univalence, starlikeness, convexity, and close-to-convexity.
Journal ArticleDOI
Starlikeness and convexity of generalized Bessel functions
TL;DR: In this article, the authors give sufficient conditions for the parameters of the normalized form of the generalized Bessel functions to be convex and star-like in the open unit disk, which is the case for the Euler gamma function.
Journal ArticleDOI
The radius of starlikeness of normalized Bessel functions of the first kind
TL;DR: In this article, the authors determined the radius of starlikeness of the normalized Bessel functions of the first kind for three different kinds of normalization and proved that the smallest positive zeros of some Dini functions are less than the first positive zero of the Bessel function.
Related Papers (5)
The radius of convexity of normalized Bessel functions
The radius of convexity of normalized Bessel functions of the first kind
Árpád Baricz,Róbert Szász +1 more