On the existence of meromorphic solutions of differential equations having arbitarily rapid growth.
On the Existence of Principal Values for the Cauchy Integral on Weighted Lebesgue Spaces for Non-Doubling Measures.
On the existence of -direction and Nevanlinna direction of -quasi-meromorphic mappings dealing with multiple values.
On the existence of Weierstrass points whose first non-gaps are five.
On the exponent of convergence for the zeros of the solutions of .
On the extendability of quadratic polynomial mappings of the plane
We shall prove, using the result from our previous paper [Ann. Polon. Math. 88 (2006)], that for a quadratic polynomial mapping Q of ℝ² only the geometric shape of the critical set of Q determines whether the complexification of Q can be extended to an endomorphism of ℂℙ². At the end of the paper we describe some interesting classes of quadratic polynomial mappings of ℝ² and give some examples.
On the Extreme Points of a Subclass of Holomorphic Functions with Positive Real Part.
On the extreme points of some classes of holomorphic functions.
On the extreme points of subordination families
We investigate extreme points of some classes of analytic functions defined by subordination and classes of functions with varying argument of coefficients. By using extreme point theory we obtain coefficient estimates and distortion theorems in these classes of functions. Some integral mean inequalities are also pointed out.
On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms.
A closed Riemann surface which is a 3-sheeted regular covering of the Riemann sphere is called cyclic trigonal, and such a covering is called a cyclic trigonal morphism. Accola showed that if the genus is greater or equal than 5 the trigonal morphism is unique. Costa-Izquierdo-Ying found a family of cyclic trigonal Riemann surfaces of genus 4 with two trigonal morphisms. In this work we show that this family is the Riemann sphere without three points. We also prove that the Hurwitz space of pairs...
On the Fekete-Szegö problem.
On the Fekete-Szegö problem for some subclasses of analytic functions.
On the Fekete-Szegő theorem for close-to-convex functions.
On the finite blocking property
A planar polygonal billiard is said to have the finite blocking property if for every pair of points in there exists a finite number of “blocking” points such that every billiard trajectory from to meets one of the ’s. Generalizing our construction of a counter-example to a theorem of Hiemer and Snurnikov, we show that the only regular polygons that have the finite blocking property are the square, the equilateral triangle and the hexagon. Then we extend this result to translation surfaces....
On the five-point theorems due to Lappan
By using an extension of the spherical derivative introduced by Lappan, we obtain some results on normal functions and normal families, which extend Lappan's five-point theorems and Marty's criterion, and improve some previous results due to Li and Xie, and the author. Also, another proof of Lappan's theorem is given.
On the fixpoints, multipliers and value distribution of certain classes of meromorphic functions.
On the fourth order root finding methods of Euler's type.
On the functional equation.
On the Gelfand-Hille theorems
On the generalization of two results of Cao and Zhang
This paper studies the uniqueness of meromorphic functions that share two values, where , , . The results significantly rectify, improve and generalize the results due to Cao and Zhang (2012).