On a class of univalent functions defined using the Sǎlǎgean differential operator with square-root component of the derivative

Abstract

UDC 517.54

We introduce a family of classes of univalent functions defined by using the Sǎlǎgean differential operator with square-root component of the derivative. We also introduce a differential operator $\mathscr V^n$ and an integral operator $\mathscr W^n$ and define a family $V^n$ of univalent functions  satisfying certain geometric conditions. Further, we present the results on inclusions, the methods used to check membership in these classes, and coefficient estimates. Moreover, we solve the Fekete–Szegö problem for these classes. Finally, we provide sharp bounds for the logarithmic coefficients of functions in $V^n.$