In the present investigation, with motivation from pioneering work of Srivastava et al. [28], which in recent years actually revived study analytic and bi-univalent functions, we introduce subclasses T*?(n,?) T?(n,?) function class ? defined open unit disk U = {z C : |z| < 1g involving S?l?gean derivative operator Dn. Moreover, derive estimates on initial coefficients |a2| |a3| for functions...

Subclasses of analytic and bi-univalent functions have been extensively improved utilized for estimating the Taylor–Maclaurin coefficients Fekete–Szegö functional. In this paper, we consider a certain subclass normalized functions. These inverses that possess continuation to an open unit disk are associated with orthogonal polynomials; namely, Gegenbauer polynomials satisfy subordination condit...

In this work, we investigate the (p, q)-Gegenbauer polynomials for a class of analytic and bi-univalent functions defined in open unit disk, with respect to subordination. We give an elementary proof establish some estimates coefficient bounds new class. conclude study by giving result Fekete-Szegö theorem. A corollary was given show results subclasses our

In the current work, we introduce a special family of function analytic and m-fold symmetric bi-univalent functions obtain estimates Taylor–Maclaurin coefficients |dm+1| |d2m+1| for in family. For ? real number, Fekete–Szegö functional |d2m+1??dm+12| is also estimated. We indicate several cases defined connections to existing results are discussed.