Bi-Univalent Condition Associated with the Modified Sigmoid Function (original) (raw)
Subclasses of Univalent Functions Involving Modified Sigmoid Function
International Journal of Difference Equations, 2021
The authors obtained some geometric results on certain new classes of analytic functions involving sigmoid function defined by Fadipe-Joseph et. al. 2016 as T γ (λ, β, α, µ). Extreme point property, radius of starlikeness and convexity, convolution property and Fekete-Szego inequality for the class were proved.
Polynomial Bounds for a Class of Univalent Function Involving Sigmoid Function
2018
In this work, a new subclass of univalent function was defined using the Sălăgean differential operator involving the modified sigmoid function and the Chebyshev polynomials. The coefficient bounds and the Fekete-Szego functional of this class were obtained using subordination principle. The results obtained agree and extend some earlier results.
COEFFICIENT ESTIMATES FOR SOME SUBCLASSES OF ANALYTIC AND Bi-UNIVALENT FUNCTIONS
2017
In the present paper, we introduce and investigate two new subclasses BΣ(α, λ, μ) andMΣ(β, λ, μ) of bi-valent functions in the unit disk U. For functions belonging to the classes BΣ(α, λ, μ) andMΣ(β, λ, μ), we obtain bounds of the first two Taylor-Maclaurin coefficients of f(z).
Coefficient Estimates for a Subclass of Analytic and Bi-Univalent Functions
Bulletin of The Iranian Mathematical Society, 2016
In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk. Upper bounds for the second and third coefficients of functions in this subclass are founded. Our results, which are presented in this paper, generalize and improve those in related works of several earlier authors.
Certain Inequalities for a General Class of Analytic and Bi-univalent Functions
In this work, the subclass S h,p Σ (λ, δ, γ) of the function class S of analytic and bi-univalent functions is defined and studied in the open unit disc. Estimates for initial coefficients of Taylor-Maclaurin series of bi-univalent functions belonging this class are obtained. Also, some relevant classes are recognized and connections to previous results are made.
Coefficient estimates for a certain subclass of analytic and bi-univalent functions
Applied Mathematics Letters, 2012
In this paper, we introduce and investigate an interesting subclass H h,p Σ of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class H h,p Σ , we obtain estimates on the first two Taylor-Maclaurin coefficients |a 2 | and |a 3 |. The results presented in this paper would generalize and improve some recent work of Srivastava et al.
New subclasses of analytic and bi-univalent functions endowed with coefficient estimate problems
2018
Inspired by the recent works of Srivastava et al. (2010), Frasin and Aouf (2011), and Caglar et al. (2013), we introduce and investigate in the present paper two new general subclasses of the class consisting of normalized analytic and bi-univalent functions in the open unit disk U. For functions belonging to these general subclasses introduced here, we obtain estimates on the Taylor-Maclaurin coefficients |a_2| and |a_3|. Several connections to some of the earlier known results are also pointed out. The results presented in this paper would generalize and improve those in related works of several earlier authors.
2020
By introducing an operator E n µ (β, λ, ω, ϕ, t)fγ (z) via a linear combination of two generalized differential operators involving modified Sigmoid function, we defined and studied certain geometric properties of a new subclass Tγ D λ,ω (α, β, µ, ω, ϕ, λ, η, ξ, t; p : n) of analytic functions in the open unit disk U. In particular, we give some properties of functions in this subclass such as; coefficient estimates, growth and distortion theorems, closure theorem and Fekete-Szego inequality for functions belonging to the subclass. Some earlier known results are special cases of results established for the new subclass defined.
Filomat, 2020
In this paper, we obtain the Fekete-Szeg? problem for the k-th (k ? 1) root transform of the analytic and normalized functions f satisfying the condition 1+ ? ??/2sin? < Re{z f'(z)/f(z)) < 1+ ?/2sin? (|z| < 1), where ? ? [?/2,?). Afterwards, by the above two-sided inequality we introduce a certain subclass of analytic and bi-univalent functions in the disk |z| < 1 and obtain upper bounds for the first few coefficients and Fekete-Szeg? problem for functions f belonging to this class.
Certain subclasses of analytic and bi-univalent functions
Applied Mathematics Letters, 2010
In the present paper, we introduce and investigate two interesting subclasses of normalized analytic and univalent functions in the open unit disk U := {z : z ∈ C and |z| < 1}, whose inverse has univalently analytic continuation to U. Among other results, bounds for the Taylor-Maclaurin coefficients |a 2 | and |a 3 | are found in our investigation.