Search

The aim of this paper is to introduce a class of starlike functions that are related to Bernoulli’s numbers of the second kind. Let φBS(ξ)=ξeξ−12=∑n=0∞ξnBn2n!, where the coefficients of Bn2 are Bernoulli numbers of the second kind. Then, we introduce a subclass of starlike functions 𝟊 such that ξ𝟊′(ξ)𝟊(ξ)≺φBS(ξ). We found out the coefficient bounds, several radii problems, structural formulas, and inclusion relations. We also found sharp Hankel determinant problems of this class.

By utilizing the concept of the q-fractional derivative operator and bi-close-to-convex functions, we define a new subclass of A, where the class A contains normalized analytic functions in the open unit disk E and is invariant or symmetric under rotation. First, using the Faber polynomial expansion (FPE) technique, we determine the lth coefficient bound for the functions contained within this class. We provide a further explanation for the first few coefficients of bi-close-to-convex functions defined by the q-fractional derivative. We also emphasize upon a few well-known outcomes of the major findings in this article.

We present a new family of s-fold symmetrical bi-univalent functions in the open unit disc in this work. We provide estimates for the first two Taylor–Maclaurin series coefficients for these functions. Furthermore, we define the Salagean differential operator and discuss various applications of our main findings using it. A few new and well-known corollaries are studied in order to show the connection between recent and earlier work.