Search

The authors propose to investigate some new criteria for a certain class of meromorphically strongly starlike functions in the punctured open unit disk. Some intriguing applications that arise as special cases of the main results, which are presented in this study, are also considered.

In the present paper, we investigated some conditions to be in the class of Carathéodory functions by using the concept of the first-order differential subordinations. Moreover, various interesting special cases were considered in the geometric function theory as applications of main results presented here. [ABSTRACT FROM AUTHOR]

In this study, a novel family of analytical functions connected to convex functions in the open unit is introduced and investigated. Additionally, relationships between this class and other subclasses of analytic functions are deduced. Further, different results for the mentioned class and several new interesting properties are obtained. [ABSTRACT FROM AUTHOR]

The objective of the present article is to introduce new subclasses of bi-Bazilevič functions, bi-quasi-convex functions and α -exponentially bi-convex functions involving functions with bounded boundary rotation of order ν. For the above-said newly defined classes, we obtain first two initial coefficient bounds. In addition, the familiar Fekete–Szegö coefficient inequality is too found for the newly introduced subclasses of bi-univalent functions. Apart from the new findings that are obtained, it also improves the prior estimates that are presented already in the literature. [ABSTRACT FROM AUTHOR]

Radii of convexity, starlikeness, lemniscate starlikeness and close-to-convexity are determined for the convex combination of the identity map and a normalized convex function F given by f(z) = α z+(1−α)F(z).

In the present paper, we give a new simple proof on the sharp bounds of coefficient functionals related to the Carathéodory functions and make a correction on the extremal functions. The result is further used to investigate some initial coefficient bounds on a subclass of bounded turning functions R ℘ associated with a cardioid domain. For functions in this class, we calculate the bounds of the Fekete–Szegö-type inequality and the second- and third-order Hankel determinants. All the results are proved to be sharp. [ABSTRACT FROM AUTHOR]

In this paper, we consider some relations related to the representations of starlike and convex functions, and obtain some sufficient conditions for starlike and convex functions by using the theory of differential subordination. Actually, we generalize a result by Suffridge for analytic functions with missing coefficients and then we apply that generalization for obtaining the different methods to the implications of starlike or convex functions. Our results generalize and improve the previous results in the literature. [ABSTRACT FROM AUTHOR]

In this study, we consider different types of convex-exponent products of elements of a certain class of log-harmonic mapping and then find sufficient conditions for them to be starlike log-harmonic functions. For instance, we show that, if f is a spirallike function, then choosing a suitable value of γ , the log-harmonic mapping F (z) = f (z) | f (z) | 2 γ is α - s p i r a l i k e of order ρ. Our results generalize earlier work in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the sharp and accurate bounds for the logarithmic coefficients of some subclasses of analytic functions defined and studied in earlier works. Furthermore, we obtain the bounds of the second Hankel determinant of logarithmic coefficients for a class defined by subordination, such as the class of starlike functions  S * (φ) . Some applications of our results, which are extensions of those reported in earlier papers are given here as special cases. In addition, the results given can be used for other popular subclasses. [ABSTRACT FROM AUTHOR]