A Note on Nevanlinna's Five Value Theorem

Abstract

Abstract. In the paper we prove a uniqueness theorem which improves and generalizes a number of uniqueness theorems for meromorphic functions related to Nevanlinna's five value theorem.

UNIQUENESS OF MEROMORPHIC FUNCTIONS SHARING VALUES WITH THEIR n-TH DERIVATIVES DILIP CHANDRA PRAMANIK AND JAYANTA ROY

“…Theorem 1[[4], p. 48] Let f (z) and g(z) be two non-constant meromorphic functions and a j ∈ C∪{∞} be distinct for j = 1, 2, ..., 5.…”

“…Theorem 5 [2] Let f and g be two non-constant meromorphic functions and a j ∈ C ∪ {∞} be distinct for j = 1, 2, ..., k (≥ 5) and for a non-negative integer n) . I. Lahiri and R. Pal [5] prove the following uniqueness theorem of meromorphic functions sharing k (≥ 5) small functions.…”

Uniqueness of Algebroid Functions in Connection to Nevanlinna’s Five-Value Theorem

“…Many researchers like Valiron [28], Baganas [1], He et al [11,12] and others have done a lot of work in this area (see [1], [4]- [6], [9]- [26], [30], [31]). In this paper, we discuss a result of Indrajit Lahiri and Rupa Pal [13] on the Nevanlinna's value distribution theory of meromorphic functions for Nevanlinna's five values theorem to algebroid functions Let A ν (z), A ν−1 (z), ..., A 0 (z) be analytic functions with no common zeros in the complex plane, then the following equation (1.1) A ν (z)W ν + A ν−1 (z)W ν−1 + ... + A 1 (z)W + A 0 (z) = 0.…”