In Geometric function theory, occasionally, attempts have been made to solve a particular problem for the Ma-Minda classes, $$\mathcal {S}^*(\psi )$$ and {C}(\psi of univalent starlike convex functions, respectively. Recently, popular radius generally known as Bohr’s phenomenon has studied in various settings; however, little is about Rogosinski radius. this article, fixed $$f\in \mathcal or ),...

In the present investigation, we use the Horadam Polynomials to establish upper bounds for the second and third coefficients of functions belongs to a new subclass of analytic and $lambda$-pseudo-starlike bi-univalent functions defined in the open unit disk $U$. Also, we discuss Fekete-Szeg$ddot{o}$ problem for functions belongs to this subclass.

The purpose of the present paper is to introduce two new subclasses of the function class ∑m  of bi-univalent functions which both f  and f-1  are m-fold symmetric analytic functions. Furthermore, we obtain estimates on the initial coefficients for functions in each of these new subclasses. Also we explain the relation between our results with earlier known results.

A necessary and sufficient coefficient is given for functions in a class of complexvalued harmonic univalent functions using the Dziok-Srivastava operator. Distortion bounds, extreme points, an integral operator, and a neighborhood of such functions are considered.

The interplay of geometry and analysis is perhaps the most fascinating aspect of complex function theory. The theory of univalent functions is concerned primarily with such relations between analytic structure and geometric behavior. A function is said to be univalent (or schlichi) if it never takes the same value twice: f(z{) # f(z2) if zx #= z2. The present survey will focus upon the class S ...