MEROMORPHIC FUNCTIONS THAT SHARE TWO OR ... - Project Euclid
Recommend Documents
derivative/7 share two finite values (counting multiplicities), then/(z) = We say two meromorphic functions f(z) and g(z) share the finite complex value c if f(z) â c ...
May 31, 1993 - ${\rm Re}\{\frac{Df(z)}{D^{n}f(z)}-2\}$. \langle. $-\frac{n+a}{n+1}$ .... $=kw(z_{O})$. ,. (2. 7) where $|w(z_{O})|$. $=1$ and $k\geq$. $1$ . From (2. 6).
Brandi Cain, Department of Mathematics, Florida Southern College,. Lakeland ... given. A problem of characterizing all vertically rigid functions remains open.
Lًf ق ¼ akًzقf ًkق akہ1ًzقf ًkہ1ق ءءء a0ًzقf , ًk b 1ق. ً1.1ق where ajًzق ًj ¼ 0, 1, ... , kق are polynomials and akًzق D 0. Indeed, we shall prove the following theorems:.
J. Inequal. Pure Appl. Math., 8 (2007), 1, Art. 18. Received 7 November 2011. West Bengal State University,. Department of Mathematics,. Barasat, 24 Prgs. (N),.
Dec 12, 1978 - Completeness Criterion or Functions with Delay. Defined over a Domain of Three Elements. By Teruo HIKITA*). Department of Mathematics ...
multipole moments exerted by the particles on the fluid and the gradients of ... Further progress can be made if the flow is axisymmetric, which happens when the ... Singular perturbation theory, valid for two spheres near touching, has also been use
Apr 20, 2005 - volving Ramanujan's theta-functions (Ð¥) for any positive real numbers ... using modular identities, transformation formulae for theta-functions.
Abstract. In this paper, we prove the functional equations for the zeta func- tions in two variables associated with prehomogeneous vector spaces acted on.
By Debika BANERJEE and Jay MEHTA. Harish Chandra ... Z x. 0 Ñx Ð tЮ. dA ÑtЮ; where A ÑxЮ ¼ A0. ÑxЮ ¼. P k x. 0 k, and the prime on the summation sign ...
the model parameter (e.g., temperature) is above the critical point and, therefore, ... caying long-range models above the critical dimension, using the lace ...
May 13, 2002 - Chlodowsky polynomials in a triangular domain. There are many ... may be found in [4, 5]. We will prove ... Let (bn) be a sequence of positive numbers with ... y) â f(x, y)| = 0 holds for all functions f which are continuous in x â¥
Libera and the author [4] and the author [5] have studied a sub- class of Σ(p), namely the class of weakly starlike meromorphic func- tions A*(p) which have the ...
uniqueness theorems to the case of meromorphic mappings of several ... some uniqueness theorems of entire functions in several complex variables and ...
GEÐ RARD KERKYACHARIAN 1,2 and DOMINIQUE PICARD2. 1UniversiteÐ Paris X-Nanterre, 200 avenue de la ReÐpublique, 92001 Nanterre Cedex, France.
Kichoon Yang an exaggeration to say that algebraic curves are responsible for
many an inspiration in other branches of mathematics. And the author's.
is analytic in |z| < r1 and p1 (0) = 1. Now differentiating (18) and with the use of. (5), we have p1 (z) â zp1 (z) p1 (z). = Dn+2f (z). Dn+1f (z) . This implies p1 (z) +.
Page 1 ... THOMAS E. CECIL AND PATRICK J. RYAN. In 1972, Nomizu and Rodriguez [5] found the following characteriza- tion of the complete umbilic ...
Two entire functions f(z) and g{z) are said to be permutable if they satisfy the ... certain differential equation and to indicate an elementary and simple method by ...
Definition 1.1: Let / and g be functions on Πto A. We say that g is conjugate of / if, for anyx, y e A, we have f(x) y =0 if, and only iί,g(y) *x = 0. If, in particular, a ...
SELF-CONJUGATE FUNCTIONS ON BOOLEAN ALGEBRAS. THOMAS A. SUDKAMP. In section 1 we investigate the properties of a self-conjugate function.
If f is s-convex, then f â = Ï f Ï, Ï â Rot( ËC), Ï â Möb(D). (1.2) is again s-convex and we have f â(D) = Ï(f(D)). The spherical and Schwarzian derivatives f # =.
MEROMORPHIC FUNCTIONS THAT SHARE TWO OR ... - Project Euclid
THEOREM B. Let f and g be meromorphic functions such that f and g share. 0, 1, oo CM. If then f-g ..... integer (^2) and α>=cos(2Ï/w)4-2*sin (2Ï/n). If f and g are ...
H.X. YI KODAI MATH. J. 13 (1990), 363—372
MEROMORPHIC FUNCTIONS THAT SHARE TWO OR THREE VALUES BY HONG-XUN Y I
1. Introduction and Main Results. Let f(z) and g{z) be two nonconstant meromorphic functions in the complex plane. If / and g have the same a -points with the same multiplicities, we say / and g share the value a CM. (see [2]). It is assumed that the reader is familiar with the fundamental concepts of Nevanlinna's theory of meromorphic functions and their standard symbols, as found in [3]. It will be convenient to let E denote any set of finite linear measure of 0 f% {II J If
{II J 2ί
(10)
{II J 3
From (6) and (10) we get D=
ft, /'.
fί, r,
and hence N(r, D)-N(r, f*)-N{r, f,)£N(r, g")-N{r, g)=2N(r, g)=2N(r, From (7), (9) and (11) we obtain
