Valence and oscillation of functions in the unit disk.
Valeurs algébriques d'une application méromorphe
Value distribution and uniqueness of difference polynomials and entire solutions of difference equations
This paper is devoted to value distribution and uniqueness problems for difference polynomials of entire functions such as fⁿ(f-1)f(z+c). We also consider sharing value problems for f(z) and its shifts f(z+c), and improve some recent results of Heittokangas et al. [J. Math. Anal. Appl. 355 (2009), 352-363]. Finally, we obtain some results on the existence of entire solutions of a difference equation of the form
Value distribution for a class of small functions in the unit disk.
Value distribution of a Wronskian.
Value distribution of certain differential polynomials.
Value distribution of meromorphic functions and their derivatives
Value distribution of meromorphic functions concerning differential polynomial.
Value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations
In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.
Value distribution problem for -adic meromorphic functions and their derivatives
In this paper we discuss the value distribution problem for -adic meromorphic functions and their derivatives, and prove a generalized version of the Hayman Conjecture for -adic meromorphic functions.
Value distributions and uniqueness of difference polynomials.
Value regions for continued fractions K(a.../1) whose elements lie in parabolic regions.
Value sharing of entire functions.
Values taken by linear combinations of cosine functions.
Value-sharing of meromorphic functions and their derivatives.
Variability regions of close-to-convex functions
M. Biernacki gave in 1936 concrete forms of the variability regions of z/f(z) and zf'(z)/f(z) of close-to-convex functions f for a fixed z with |z|<1. The forms are, however, not necessarily convenient to determine the shape of the full variability region of zf'(z)/f(z) over all close-to-convex functions f and all points z with |z|<1. We propose a couple of other forms of the variability regions and see that the full variability region of zf'(z)/f(z) is indeed the complex plane minus the origin....
Variability sets on Riemann surfaces and forgetful maps between Teichmüller spaces.
Variable exponent Fock spaces
We introduce variable exponent Fock spaces and study some of their basic properties such as boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality. We also prove that under the global log-Hölder condition, the variable exponent Fock spaces coincide with the classical ones.
Varianten des Schwarzschen Lemma.
Variation of quasiconformal mappings on lines
We obtain improved regularity of homeomorphic solutions of the reduced Beltrami equation, as compared to the standard Beltrami equation. Such an improvement is not possible in terms of Hölder or Sobolev regularity; instead, our results concern the generalized variation of restrictions to lines. Specifically, we prove that the restriction to any line segment has finite p-variation for all p > 1 but not necessarily for p = 1.