In this work, applying a lemma due to Nunokawa et al. (J. Ineq. Appl. 2015. 1 (2015)  7), we obtain some sufficient inequalities for some certain subclasses of UNIVALENT FUNCTIONS.

In this paper, we define and investigate a new class of spirallike harmonic FUNCTIONS defined by a Salagean differential operator and we obtain a coefficient inequality for the FUNCTIONS in this class. Following, we investigated convolution and obtain the order of convolution consistence for certain spirallike harmonic UNIVALENT FUNCTIONS with negative coefficients.

In this paper, the problem of stability for certain subclasses of harmonic UNIVALENT FUNCTIONS is investigated. Some lower bounds for the radius of stability of these subclasses are found.

In the present investigation, our main aim is to introduce a certain subclass of analytic UNIVALENT FUNCTIONS related to the Error function. We discuss the implications of our main results, including the coefficient bound, extreme points, weighted mean, convolution, convexity, and radii properties, as well as any other related properties.

Let 𝝨 be the class of meromorphic bi-UNIVALENT FUNCTIONS f of the formf(z)=z+b_0+∑ _(n=1)^∞ ▒ b_n/z^n, which are UNIVALENT (analytic and one to one) on the domain Δ ={z∈ C∶ 1.

In the present investigation, we use the Horadam Polynomials to establish upper bounds for the second and third coe, cients of FUNCTIONS belongs to a new subclass of analytic and ,-pseudo-starlike bi-UNIVALENT FUNCTIONS de, ned in the open unit disk U. Also, we discuss Fekete-Szeg, o problem for FUNCTIONS belongs to this subclass.

In the present paper, we obtain some subordination and superordination results involving the Hadamard product operator $D^{\mu,b}_{\alpha,c}$ for certain normalized analytic UNIVALENT FUNCTIONS in the open unit disk. These results are applied to obtain sandwich results.

The purpose of the present paper is to introduce and investigate two new subclasses KΣ m(λ , γ ; α ) and K∗ Σ m (λ , γ ; β ) of Σ m consisting of analytic and m-fold symmetric bi-UNIVALENT FUNCTIONS defined in the open unit disk U. We obtain upper bounds for the coefficients |am+1| and |a2m+1| for FUNCTIONS belonging to these subclasses. Many of the well-known and new results are shown to follow as special cases of our results.

By using a certain operator Sn, we introduce a class of holomorphic FUNCTIONS Sn(b), and obtain some subordination results. We also show that the set Sn(b) is convex and obtain some new differential subordinations related to certain integral operators.