BOUNDS FOR THE RADII OF UNIVALENCE OF SOME SPECIAL FUNCTIONS

被引：30
作者：
Aktas, Ibrahim [1 ]
Baricz, Arpad [2 ,3 ]
Yagmur, Nihat [4 ]
机构：
[1] Gumushane Univ, Dept Math Engn, Fac Engn & Nat Sci, TR-29100 Gumushane, Turkey
[2] Babes Bolyai Univ, Dept Econ, Cluj Napoca 400591, Romania
[3] Obuda Univ, Inst Appl Math, H-1034 Budapest, Hungary
[4] Erzincan Univ, Fac Arts & Sci, Dept Math, TR-24000 Erzincan, Turkey
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2017年 / 20卷 / 03期
关键词：
Lommel; Struve and Bessel functions; univalent; starlike functions; radius of univalence and starlikeness; zeros of Lommel; Mittag-Leffler expansions; Laguerre-Polya class of entire functions; NORMALIZED BESSEL-FUNCTIONS; GEOMETRIC-PROPERTIES; CONVEXITY; STARLIKENESS;
D O I：
10.7153/mia-20-52
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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-Polya class of entire functions plays an important role in our study.
引用
收藏
页码：825 / 843
页数：19
相关论文
共 25 条
  • [1] [Anonymous], 2010, Handbook of Mathematical Functions
  • [2] Baricz A., 2006, Mathematica, V48, P13
  • [3] Baricz A, 2010, Lecture Notes in Mathematics, DOI DOI 10.1007/978-3-642-12230-9
  • [4] Baricz A, 2008, PUBL MATH-DEBRECEN, V73, P155
  • [5] Geometric properties of some Lommel and Struve functions
    Baricz, Arpad
    Yagmur, Nihat
    [J]. RAMANUJAN JOURNAL, 2017, 42 (02) : 325 - 346
  • [6] Turan type inequalities for Struve functions
    Baricz, Arpad
    Ponnusamy, Saminathan
    Singh, Sanjeev
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 445 (01) : 971 - 984
  • [7] TURAN-TYPE INEQUALITIES FOR SOME LOMMEL FUNCTIONS OF THE FIRST KIND
    Baricz, Arpad
    Koumandos, Stamatis
    [J]. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2016, 59 (03) : 569 - 579
  • [8] RADII OF STARLIKENESS OF SOME SPECIAL FUNCTIONS
    Baricz, Arpad
    Dimitrov, Dimitar K.
    Orhan, Halit
    Yagmur, Nihat
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (08) : 3355 - 3367
  • [9] Baricz A, 2016, COMPUT METH FUNCT TH, V16, P93, DOI 10.1007/s40315-015-0123-1
  • [10] Close-to-Convexity of Some Special Functions and Their Derivatives
    Baricz, Arpad
    Szasz, Robert
    [J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2016, 39 (01) : 427 - 437
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