Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions

Abstract

Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g = f −1 satisfying the conditions that zf ′ (z)/f (z) and zg ′ (z)/g(z) are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are made.

The Fekete-Szegö functional problems for some subclasses of m-fold symmetric bi-univalent functions

“…In this paper, we introduce several new subclasses of the class of m -fold symmetric bi-univalent functions and obtain estimates of the Taylor-Maclaurin coefficients |a m+1 | , |a 2m+1 | and Fekete-Szegö functional problems for functions in these new subclasses. The results presented in this paper improve the earlier results of Ali et al [1], Frasin and Aouf [6], and Srivastava et al [14] in terms of the bounds as well as the ranges of the parameter under consideration. Our results also further generalize the results of Peng et al [19].…”

Certain classes of bi-univalent functions with bounded boundary variation

“…Various subclasses of the bi-univalent function class Σ were introduced and non-sharp estimates on the first two coefficients |a 2 | and |a 3 | in the Taylor-Maclaurin series expansion (1.1) were found in several recent investigations (see, for example, [1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,19,21,22,23,24,25,26,27,29,30,31,32,33,34,35] and references therein). The aforecited all these papers on the subject were actually motivated by the pioneering work of Srivastava et al [28].…”

Generalized Differential Operator on Bistarlike and Biconvex Functions Associated By Quasi-Subordination

“…this class was studied by Ali et al [11,12]. In special case for =1,b=d and =0, we have the class ℳ , 0 ( , , 1, ϕ) = ,  (ϕ), was introduced by Goyal and Kumar [10].We observe that, for ( ) ≡ 1, we get the class…”