Abstract
Let \(\Omega\) denote the class of functions f analytic in the open unit disc \(\Delta\), normalized by the condition \(f(0)=f'(0)-1=0\) and satisfying the inequality
The class \(\Omega\) was introduced recently by Peng and Zhong (Acta Math Sci 37B(1):69–78, 2017). Also let \({\mathcal {U}}\) denote the class of functions f analytic and normalized in \(\Delta\) and satisfying the condition
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 \({\mathcal {U}}\), the radius of starlikeness, convexity and close–to–convexity and sufficient condition for function f to be in \(\Omega\). Furthermore, along with the settlement of the coefficient problem and the Fekete–Szegö problem for the elements of \(\Omega\), the Toeplitz matrices for \(\Omega\) are also discussed in this article.
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We thank the anonymous reviewer for his/her careful reading of our manuscript and his/her comments and suggestions.
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Communicated by Kaushal Verma.
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Mahzoon, H., Kargar, R. Further results for a subclass of univalent functions related with differential inequality. Indian J Pure Appl Math 52, 205–215 (2021). https://doi.org/10.1007/s13226-021-00071-2
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DOI: https://doi.org/10.1007/s13226-021-00071-2