Generalized integral operator and multivalent functions.
Generalized problem of starlikeness for products of close-to-star functions
We consider functions of the type , where are real numbers and are -strongly close-to-starlike functions of order . We look for conditions on the center and radius of the disk (a,r) = z:|z-a| < r, |a| < r ≤ 1 - |a|, ensuring that F((a,r)) is a domain starlike with respect to the origin.
Growth of entire functions with some univalent Gelfond-Leontev derivatives.
Harmonic starlike functions of complex order involving hypergeometric functions
Harmonic univalent functions defined by an integral operator.
Hermitian-Toeplitz determinants and some coefficient functionals for the starlike functions
In this paper, we have determined the sharp lower and upper bounds on the fourth-order Hermitian-Toeplitz determinant for starlike functions with real coefficients. We also obtained the sharp bounds on the Hermitian-Toeplitz determinants of inverse and logarithmic coefficients for starlike functions with complex coefficients. Sharp bounds on the modulus of differences and difference of moduli of logarithmic and inverse coefficients are obtained. In our investigation, it has been found that the bound...
Hyperbolically convex functions
We investigate univalent holomorphic functions f defined on the unit disk 𝔻 such that f(𝔻) is a hyperbolically convex subset of 𝔻; there are a number of analogies with the classical theory of (euclidean) convex univalent functions. A subregion Ω of 𝔻 is called hyperbolically convex (relative to hyperbolic geometry on 𝔻) if for all points a,b in Ω the arc of the hyperbolic geodesic in 𝔻 connecting a and b (the arc of the circle joining a and b which is orthogonal to the unit circle) lies in...
Hyperbolically convex functions II
Unlike those for euclidean convex functions, the known characterizations for hyperbolically convex functions usually contain terms that are not holomorphic. This makes hyperbolically convex functions much harder to investigate. We give a geometric proof of a two-variable characterization obtained by Mejia and Pommerenke. This characterization involves a function of two variables which is holomorphic in one of the two variables. Various applications of the two-variable characterization result in...
Inclusion relationships between classes of functions defined by subordination
The purpose of the present paper is to investigate various inclusion relationships between several classes of analytic functions defined by subordination. Many interesting applications involving the well-known classes of functions defined by linear operators are also considered.
Inequalities involving multipliers for multivalent harmonic functions.
Inequalities of Grunsky-Nehari type for pairs of vector functions
Initial coefficients for generalized subclasses of bi-univalent functions defined with subordination
This paper is concerned with certain generalized subclasses of bi-univalent functions defined with subordination in the open unit disc . The bounds for the initial coefficients for the functions in these classes are studied. The earlier known results follow as special cases.
Initial Maclaurin coefficient estimates for -pseudo-starlike bi-univalent functions associated with Sakaguchi-type functions
We introduce and study two certain classes of holomorphic and bi-univalent functions associating -pseudo-starlike functions with Sakaguchi-type functions. We determine upper bounds for the Taylor–Maclaurin coefficients and for functions belonging to these classes. Further we point out certain special cases for our results.
Linear Combinations of Regular Functions with Negative Coefficients
Local inequalities for some functionals in the class S
Loewner-type approximations for convex functions
Logarithmic coefficients of univalent functions.
Meromorphic functions with positive coefficients.
Meromorphic starlike functions of order with alternating coefficients
Meromorphic starlike univalent functions with alternating coefficients.