Let 𝕂 be a complete and algebraically closed non-Archimedean valued field. Following ideas of Marc Krasner and Philippe Robba, we define K-meromorphic functions from 𝕂 to 𝕂. We show that the Nevanlinna theory for functions of a single complex variable may be extended to those functions (and consequently to meromorphic functions).
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
The paper concerns interesting problems related to the field of Complex Analysis, in particular Nevanlinna theory of meromorphic functions. The author have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a small function without counting multiplicity. The results of this paper are extension of some problems studied by K. Boussaf et. al. in [2] and generalization of some results of S.S. Bhoosnurmath et. al. in [4].
3
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
In this paper, we shall investigate the existence of finite order entire and meromorphic solutions of linear difference equation of the form fn(z)+p(z)fn-2(z)+L(z, f)=h(z) where L(z, f) is linear difference polynomial in f(z), p(z) is non-zero polynomial and h(z) is a meromorphic function of finite order. We also consider finite order entire solution of linear difference equation of the form fn(z)+p(z)L(z, f)-r(z)eq(z) where r(z) and q(z) are polynomials.
4
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
With the help of the Nevanlinna theory of meromorphic functions, the purpose of this article is to describe the existence and the forms of transcendental entire and meromorphic solutions for several systems of the quadratic trinomial functional equations: {f(z)2+2αf(z)g(z+c)+g(z+c)2=1,g(z)2+2αg(z)f(z+c)+f(z+c)2=1, {f(z+c)2+2αf(z+c)g'(z)+g'(z)2=1,g(z+c)2+2αg(z+c)f'(z)+f'(z)2=1, and {f(z+c)2+2αf(z+c)g′′(z)+g′′(z)2=1,g(z+c)2+2αg(z+c)f′′(z)+f′′(z)2=1. We obtain a series of results on the forms of the entire solutions with finite order for such systems, which are some improvements and generalizations of the previous theorems given by Gao et al. Moreover, we provide some examples to explain the existence and forms of solutions for such systems in each case.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.