In this article we define a class of starlike functions with respect to symmetric points in the domain sine function. Also, investigate coefficients bounds and upper for third order Hankel determinant defined class. We also evaluate Zalcman functional \(|a_{3}^{2}-a_{5}|\). Specializing parameters, improve functions.

The Carlson-Shaffer operator L(a, c)f = φ(a, c) ∗ f, where f(z) = z+ a2z + · · · is analytic in the unit disk E = {z : |z| < 1} and φ(a, c; z) is an incomplete beta function, is used to define the class T (a, c). An analytic function f belongs to T (a, c) if L(a, c)f is starlike in E. The object of the present paper is to derive some properties of functions f in the class T (a, c).

Let Ss*(ez) denote the class of starlike functions with respect to symmetric points subordinate exponential function, i.e., which satisfy in unit disk U condition 2zf′(z)f(z)−f(−z)≺ez(z∈U). We obtained sharp estimate second-order Hankel determinants H2,3(f) and improved third-order H3,1(f) for this Ss*(ez).

In this paper, our main focus is to define a new subfamily of q-analogue analytic functions associated with the q-cosine function. Furthermore, we investigate some useful results such as necessary and sufficient condition based on convolution idea, growth distortion bounds, closure theorem, convex combination, radii starlikeness, extreme point theorem partial sums for newly-defined class.

The purpose of this paper is to apply Wright generalized hypergeometric (Wgh) functions in defining a linear operator and obtain some inclusion relationships between the classes of harmonic univalent functions under this linear operator whenever certain Wgh inequalities with its validity conditions hold. Results for special cases of Wgh functions are also mentioned. 2000 Mathematics Subject Cla...

Let ∑ p be the class of functions f(z) which are analytic in the punctured disk E∗ = {z ∈ C : 0 < |z| < 1}. Applying the linear operator Dn+p defined by using the convolutions, the subclass n+p(α) of ∑ p is considered. The object of the present paper is to prove that n+p(α) ⊂ n+p−1(α). Since 0(α) is the class of meromorphic p-valent starlike functions of order α, all functions in n+p−1(α) are m...

In numerous geometric and physical applications of complex analysis, estimating the sharp bounds coefficient-related problems univalent functions is very important due to fact that these coefficients describe core inherent properties conformal maps. The primary goal this paper was calculate estimates initial some their combinations (the Hankel determinants, Zalcman’s functional, etc.) for class...

In the current work, we use (M,N)-Lucas Polynomials to introduce a new family of holomorphic and bi-univalent functions which involve linear combination between Bazilevic ?-pseudo-starlike function defined in unit disk D establish upper bounds for second third coefficients belongs this family. Also, discuss Fekete-Szeg? problem