A1 Refereed original research article in a scientific journal
Further results for a subclass of univalent functions related with differential inequality
Authors: Mahzoon Hesam, Kargar Rahim
Publisher: INDIAN NAT SCI ACAD
Publication year: 2021
Journal: Indian Journal of Pure and Applied Mathematics
Journal acronym: INDIAN J PURE AP MAT
Volume: 52
Issue: 1
First page : 205
Last page: 215
Number of pages: 11
ISSN: 0019-5588
eISSN: 0975-7465
DOI: https://doi.org/10.1007/s13226-021-00071-2
Abstract
Let Omega denote the class of functions f analytic in the open unit disc D, normalized by the condition f(0) = f' (0) - 1 = 0 and satisfying the inequalityvertical bar zf'(z) - f(z)vertical bar 1/2 (z is an element of Delta).The class Omega was introduced recently by Peng and Zhong (Acta Math Sci 37B(1):69-78, 2017). Also let U denote the class of functions f analytic and normalized in Delta and satisfying the conditionvertical bar(z/f(z)(2) f'(z) - vertical bar< 1 (z is an element of Delta).In this article, we obtain some further results for the class Omega including, an extremal function and more examples of Omega, inclusion relation between Omega and U, the radius of starlikeness, convexity and close-toconvexity and sufficient condition for function f to be in Omega. Furthermore, along with the settlement of the coefficient problem and the Fekete-Szego problem for the elements of Omega, the Toeplitz matrices for Omega are also discussed in this article.
Let Omega denote the class of functions f analytic in the open unit disc D, normalized by the condition f(0) = f' (0) - 1 = 0 and satisfying the inequalityvertical bar zf'(z) - f(z)vertical bar 1/2 (z is an element of Delta).The class Omega was introduced recently by Peng and Zhong (Acta Math Sci 37B(1):69-78, 2017). Also let U denote the class of functions f analytic and normalized in Delta and satisfying the conditionvertical bar(z/f(z)(2) f'(z) - vertical bar< 1 (z is an element of Delta).In this article, we obtain some further results for the class Omega including, an extremal function and more examples of Omega, inclusion relation between Omega and U, the radius of starlikeness, convexity and close-toconvexity and sufficient condition for function f to be in Omega. Furthermore, along with the settlement of the coefficient problem and the Fekete-Szego problem for the elements of Omega, the Toeplitz matrices for Omega are also discussed in this article.
UTU Research Portal