In the present paper, we investigate two new subclasses 〖AR〗_(Σ_m ) (δ,λ;α) and 〖AR〗_(Σ_m ) (δ,λ;β) of Σ_m consisting of m-fold symmetric holomorphic bi-univalent functions in the open unit disk Δ. For functions from the two classes described here, we obtain estimates on the initial bounds |d_(m+1) | and |d_(2m+1) |. In addition, we get new special cases for our results.
In the present paper, we define a new class NA(n,p,λ,α,β) of multivalent functions which are holomorphic in the unit disk ∆ ={s∈C∶|s|<1}. A necessary and sufficient condition for functions to be in the class NA(n,p,λ,α,β) is obtained. Also, we get some geometric properties like radii of starlikeness, convexity and close-to-convexity, closure theorems, extreme points, integral means inequalities and integral operators.
In the present work, we submit and study a new class AN(τ, λ, η, ρ) containing holomorphic univalent functions defined by linear operator in the open unit disk Λ={s ϵ C :|s | <1} We get some geometric properties, such as, coefficient inequality, growth, and distortion bounds, convolution properties, convex set, neighborhood property, radii of starlikeness and convexity , weighted mean and arithmetic mean for functions belonging to the class AN(τ, λ, η, ρ)
The aim of the present paper is to introduce a certain families of holomorphic and Sălăgean type bi-univalent functions by making use (p, q) - Lucas polynomials involving the modified sigmoid activation function Φ(δ)=z/(1+e-δ) δ>=1 in the open unit disk Λ. For functions belonging to these subclasses, we obtain upper bounds for the second and third coefficients. Also, we debate Fekete-Szegö inequality for these families. Further, we point out several certain special cases for our results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.