Nevanlinna’s Five Values Theorem on Annuli

Abstract

By using the second main theorem of the meromorphic function on annuli, we investigate the problem on two meromorphic functions partially sharing five or more values and obtain some theorems that improve and generalize the previous results given by Cao and Yi.

Unicity Theorem for Higher Order Derivatives of Meromorphic Functions on Annuli Dilip Chandra Pramanik and Jayanta Roy

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In this paper, we deal with the uniqueness problem for higher order derivatives of meromorphic functions on annuli. Our results generalize the result given by H. Y. Xu and H. Wang [18].

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“…In 2016 H. Y. Xu and H. Wang [18] investigated the uniqueness of meromorphic functions on annuli and proved the following results: Theorem 4. Let f and g be two transcendental or admissible meromorphic functions on the annulus A = {z : 1 R0 < |z| < R 0 }, where 1 < R 0 ≤ +∞.…”

Five Value Theorem Applied to Derivatives on Annuli Shilpa N.

“…In Recent years, Nevanlinna theory of meromorphic functions on the annulus(doublyconnected region) became the hot topic of research( see [4,5,6,9,10,11,12,13]).…”

“…Also in E k) (a, f ) the set of zeros of f − a with multiplicities no greater than k, each zero is counted only once. In 2016, Hong-Yan and Hua Wang [9] investigated the following problem on two meromorphic functions partially sharing five or more values.…”