Initial coefficients for generalized subclasses of bi-univalent functions defined with subordination

summary:This paper is concerned with certain generalized subclasses of bi-univalent functions defined with subordination in the open unit disc $E=\left\rbrace z:\mid z \mid <1\right\lbrace$. The bounds for the initial coefficients for the functions in these classes are studied. The earlier known results follow as special cases

Geometrical Theory of Analytic Functions

The book contains papers published in the Mathematics Special Issue, entitled "Geometrical Theory of Analytic Functions". Fifteen papers devoted to the study concerning complex-valued functions of one variable present new outcomes related to special classes of univalent functions, differential equations in view of geometric function theory, quantum calculus and its applications in geometric function theory, operators and special functions associated with differential subordination and superordination theories and starlikeness, and convexity criteria

A Subclass of Bi-Univalent Functions Defined by Generalized Sãlãgean Operator Related to Shell-Like Curves Connected with Fibonacci Numbers

The aim of this paper is to study certain subclasses of bi-univalent functions defined by generalized Sãlãgean differential operator related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients a2 and a3 and upper bounds for the Fekete-Szegö functional for the functions in this class. The results proved by various authors follow as particular cases