In this paper, some coefficient problems for starlike analytic functions with respect to symmetric points are considered. Bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates for the following: coefficients, logarithmic coefficients, some cases of the generalized Zalcman coefficient functional, and some cases of the Hankel determinant.
In the present paper, the authors implement the two analytic functions with its positive real part in the open unit disk. New types of polynomials are introduced, and by using these polynomials with the Faber polynomial expansion, a formula is structured to solve certain coefficient problems. This formula is applied to a certain class of bi-univalent functions and solve the
n
-th term of its coefficient problems. In the last section of the article, several well-known classes are also extended to its
n
-th term.
We define a classT̃k[A, B,α,ρ] of analytic functions by using Janowski’s functions which generalizes a number of classes studied earlier such as the class of strongly close-to-convex functions. Some properties of this class, including arc length, coefficient problems, and a distortion result, are investigated. We also discuss the growth of Hankel determinant problem.
We define and study some subclasses of analytic functions by using a certain multiplier transformation. These functions map the open unit disc onto the domains formed by parabolic and hyperbolic regions and extend the concept of uniformly close-to-convexity. Some interesting properties of these classes, which include inclusion results, coefficient problems, and invariance under certain integral operators, are discussed. The results are shown to be the best possible.
A class of analytic functions is denoted by M. Furthermore, S⸦M includes of analytic, normalized and univalent functions. The main -subclasses of S are starlike functions, S and convex functions, S* . Recently, many mathematicians studied about the q-derivative operator. Inspired by the ideas from some previous works, we introduce another two new subclasses of M . The coefficient problems in particular the upper bounds of the Fekete-Szegö (F-S) functional for these subclasses were obtained.
On Coefficient Problems for Functions Connected with the Sine Function
