Further results for a subclass of univalent functions related with differential inequality

: Mahzoon Hesam, Kargar Rahim

Publisher: INDIAN NAT SCI ACAD

: 2021

: Indian Journal of Pure and Applied Mathematics

: INDIAN J PURE AP MAT

: 52

: 1

: 205

: 215

: 11

: 0019-5588

: 0975-7465

DOI: https://doi.org/10.1007/s13226-021-00071-2

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.