The aim of this paper is to introduce some special families of holomorphic and Sălăgean type bi-univalent functions by making use of Horadam polynomials involving the modified sigmoid activation function ϕ(s) = 2 1+e −s , s ≥ 0 in the open unit disc D. We investigate the upper bounds on initial coefficients for functions of the form g ϕ (z) = z+ ∞ j=2 ϕ(s)d j z j , in these newly introduced special families and also discuss the Fekete-Szegö problem. Some interesting consequences of the results established here are also indicated.
In this paper we consider two subclasses of bi-univalent functions defined by the Horadam polynomials. Further, we obtain coefficient estimates for the defined classes.
In this paper, we introduce a special family Mσm(τ,ν,η,φ) of the function family σm of m-fold symmetric bi-univalent functions defined in the open unit disc D and obtain estimates of the first two Taylor–Maclaurin coefficients for functions in the special family. Further, the Fekete–Szegö functional for functions in this special family is also estimated. The results presented in this paper not only generalize and improve some recent works, but also give new results as special cases.
The object of this article is to explore two subclasses of regular and bi-univalent functions subordinate to Horadam polynomials in the disk $\{\varsigma\in\mathbb{C}:|\varsigma| <1\}$. We originate upper bounds for the initial Taylor-Maclaurin coefficient estimates of functions in these subclasses. Fekete-Szeg\"o functional problem is also established. Furthermore, we present some new observations and investigate relevant connections to existing results.
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