Differential Subordinations for Nonanalytic Functions

被引:0
|
作者
Oros, Georgia Irina [1 ]
Oros, Gheorghe [1 ]
机构
[1] Univ Oradea, Dept Math, Oradea 410087, Romania
关键词
D O I
10.1155/2014/251265
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In the paper by Mocanu (1980), Mocanu has obtained sufficient conditions for a function in the classes C-1(U), respectively, and C-2(U) to be univalent and to map U onto a domain which is starlike (with respect to origin), respectively, and convex. Those conditions are similar to those in the analytic case. In the paper by Mocanu (1981), Mocanu has obtained sufficient conditions of univalency for complex functions in the class C-1 which are also similar to those in the analytic case. Having those papers as inspiration, we try to introduce the notion of subordination for nonanalytic functions of classes C-1 and C-2 following the classical theory of differential subordination for analytic functions introduced by Miller and Mocanu in their papers (1978 and 1981) and developed in their book (2000). Let Omega be any set in the complex plane C, let p be a nonanalytic function in the unit disc U, p is an element of C-2(U) and let psi(r, s, t; z) : C-3 x U -> C. In this paper, we consider the problem of determining properties of the function p, nonanalytic in the unit disc U, such that p satisfies the differential subordination psi(p(z), Dp(z), D-2 p(z) - Dp(z);z) subset of Omega double right arrow p(U) subset of Delta.
引用
收藏
页数:9
相关论文
共 50 条
  • [41] Some differential subordinations and fuzzy differential subordinations using generalized integral operator
    Naik, Uday H.
    Shaikh, Raisa M.
    Gophane, Machchhindra T.
    Wanas, Abbas K.
    ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2023, (48): : 830 - 842
  • [42] NEW FUZZY DIFFERENTIAL SUBORDINATIONS
    Oros, Georgia Irina
    COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2021, 70 (01): : 229 - 240
  • [43] Differential subordinations and argument inequalities
    Liu, Jin-Lin
    Ahuja, Om P.
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2010, 347 (08): : 1430 - 1436
  • [44] ON MAPPINGS DEFINED BY NONANALYTIC FUNCTIONS
    GONZALEZ, MO
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 17 (01): : 159 - &
  • [45] Third-Order Differential Subordinations for Analytic Functions Associated with Generalized Mittag-Leffler Functions
    Dorina Răducanu
    Mediterranean Journal of Mathematics, 2017, 14
  • [46] Briot-Bouquet Differential Subordinations for Analytic Functions Involving the Struve Function
    Cetinkaya, Asena
    Cotirla, Luminita-Ioana
    FRACTAL AND FRACTIONAL, 2022, 6 (10)
  • [47] On second-order differential subordinations for a class of analytic functions defined by convolution
    Akgul, Arzu
    JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (03): : 954 - 963
  • [48] DIFFERENTIAL SUBORDINATIONS AND PYTHAGOREAN MEANS
    Gavris, Eszter
    MATHEMATICA SLOVACA, 2020, 70 (05) : 1135 - 1140
  • [49] Differential Subordinations and Harmonic Means
    Kanas, Stanisawa
    Tudor, Andreea-Elena
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2015, 38 (03) : 1243 - 1253
  • [50] Differential Subordinations and Harmonic Means
    Stanisława Kanas
    Andreea-Elena Tudor
    Bulletin of the Malaysian Mathematical Sciences Society, 2015, 38 : 1243 - 1253