Radii of starlikeness of some special functions

Baricz, Árpád; Dimitrov, Dimitar K.; Orhan, Halit; Yağmur, Nihat

doi:10.1090/proc/13120

Cited by 44 publications

(38 citation statements)

References 15 publications

(3 reference statements)

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“…2 (z) = 0 is actually the radius of starlikeness of g µ , according to [4]. These show that indeed the radius of univalence corresponds to the radius of starlikeness of the function g µ .…”

Section: Proofs Of the Resultsmentioning

confidence: 75%

“…where u n > 0 and n≥1 u −2 n < ∞, then the radii of univalence and starlikeness of f coincide and are equal to the smallest positive zero of f ′ . Thus, applying this result to the normalized Struve function v ν it follows that indeed r ⋆ (v ν ) is the radius of univalence and starlikeness, which according to [4] it is the smallest positive root of the transcendental equation zH ′ ν (z) − νH ν (z) = 0. b. We proceed exactly as in the proof of Theorem 1 about the radius of univalence of normalized Bessel function discussed therein.…”

Section: Proofs Of the Resultsmentioning

confidence: 84%

See 1 more Smart Citation

Bounds for the radii of univalence of some special functions

Aktaş

Baricz

Yağmur

2017

Mathematical Inequalities &Amp; Applications

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Abstract. Tight lower and upper bounds for the radii of univalence (and starlikeness) of some normalized Bessel, Struve and Lommel functions of the first kind are obtained via Euler-Rayleigh inequalities. It is shown also that the radius of univalence of the Struve functions is greater than the corresponding radius of univalence of Bessel functions. Moreover, by using the idea of Kreyszig and Todd, and Wilf it is proved that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions, and they are actually solutions of some functional equations. The Laguerre-Pólya class of entire functions plays an important role in our study.Mathematics subject classification (2010): 30C45, 30C15, 33C10.

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Section: Proofs Of the Resultsmentioning

confidence: 75%

Section: Proofs Of the Resultsmentioning

confidence: 84%

Bounds for the radii of univalence of some special functions

Aktaş

Baricz

Yağmur

2017

Mathematical Inequalities &Amp; Applications

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“…Recently, there has been a vivid interest on some geometric properties such as univalency, starlikeness, convexity and uniform convexity of various special functions such as Bessel, Struve, Lommel, Wright and q-Bessel functions (see [1,2,3,4,7,8,9,10,11,15,16,13,17]). In the above mentioned papers the authors have used frequently some properties of the zeros of these functions.…”

Section: Introductionmentioning

confidence: 99%

Geometric and monotonic properties of hyper-Bessel functions

2019

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Some geometric properties of a normalized hyper-Bessel functions are investigated. Especially we focus on the radii of starlikeness, convexity, and uniform convexity of hyper-Bessel functions and we show that the obtained radii satisfy some transcendental equations. In addition, we give some bounds for the first positive zero of normalized hyper-Bessel functions, Redheffer-type inequalities, and bounds for this function. In this study we take advantage of Euler-Rayleigh inequalities and Laguerre-Pólya class of real entire functions, intensively.2010 Mathematics Subject Classification. 30C45, 30C15, 33C10. Key words and phrases. Starlike, convex and uniformly convex functions; radius of starlikeness, convexity and uniform convexity; hyper-Bessel functions; zeros of hyper-Bessel functions; Laguerre-Pólya class of entire functions.

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“…Struve functions are applied to various areas of applied mathematics and physics. In [10], and the reference therein various applications are illustrated in different context and also for its application in geometric function theory we refer [2], [8], [9], [11], [12], etc. Let S p denote the Struve function of order p is of the form…”

Section: Introductionmentioning

confidence: 99%