Refereed journal article or data article (A1)

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

List of 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 number: 52

Issue number: 1

Number of pages: 11

ISSN: 0019-5588

eISSN: 0975-7465

DOI: http://dx.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.