The object of this article is to explore a ?-pseudo-?-convex ?-fold symmetric bi-univalent function family satisfying subordinations condition generalizing certain previously examined families. We originate the initial Taylor–Maclaurin coefficient estimates functions in defined family. classical Fekete–Szegö inequalities for also estimated. Furthermore, we present some special cases main result...

In this paper, we intorduce a family of analytic functions in the open unit disk which is bi-univalent. By virtue Faber polynomial expansions, estimation n?th(n?3) Taylor–Maclaurin coefficients an obtained. Furthermore, bounds value first two such established.

In the contemporary paper, we introduce new subclasses of analytic and bi-univalent functions involving integral operator based upon Lucas polynomial. Furthermore, find estimates on first two Taylor-Maclaurin coefficients a2 a3 for in these obtain Fekete-Szegö problem subclasses.

Three subclasses of analytic and bi-univalent functions are introduced through the use q?Gegenbauer polynomials, which a generalization Gegenbauer polynomials. For falling within these subclasses, coefficient bounds a2 a3 as well Fekete–Szegö inequalities derived. Specializing parameters used in our main results leads to number new results.

  , T For real numbers  and  such that 0 1      , we denote by   the class of normalized analytic functions which satisfy     Re f z     z   , T   , where denotes the open unit disk. We find some relationships involving functions in the class      . And we estimate the bounds of coefficients and solve Fekete-Szegö problem for functions in this class. Furthermore, we...