Simple criteria for univalence and coefficient bounds for a certain subclass of analytic functions

Abstract

In the …rst part of this work we present several new geometric properties of analytic functions by applying the di¤erential subordination. In addition, several results in the geometric functions theory pointed out. In the second part we …nd upper bounds for coe¢ cients of functions in class B q; ( ; ; h) which is de…ned by fractional q-calculus operators. c 2 0 2 0 A n ka ra U n ive rsity C o m m u n ic a tio n s Fa c u lty o f S c ie n c e s U n ive rsity o f A n ka ra -S e rie s A 1 M a th e m a tic s a n d S ta tistic s where D q;z f in (1.3) represents, respectively, a fractional q-integral of f of order when 1 < < 0, and a fractional q-derivative of f of order when 0 < 2.

Coefficient Bounds for Some Families of Bi-Univalent Functions with Missing Coefficients

“…In a few of these articles, the authors studied some subclasses of bi-univalent functions connected with the Faber and Laguerre polynomials, determined estimates for coefficients and Hankel determinants for different subclasses of bi-univalent functions associated with Hohlov operator and Horadam polynomials, and gave some estimates for the Fekete-Szegő functional. Other related issues can be found in [14][15][16], while, in general, it is still difficult to determine the extremal functions for bi-univalent functions.…”

Coefficient estimates for a subclass of analytic functions by Srivastava-Attiya operator

“…Let Σ denote the class of bi-univalent functions in U given by (1.1). Recently many researchers have introduced and investigated several interesting subclasses of the bi-univalent function class Σ and they have found non-sharp estimates on the first two Taylor-Maclaurin coefficients |a 2 | and |a 3 | and other problems, see for example, [3,2,4,5,6,7,8,10,11,13,14,15,22,23,24].…”