Uniqueness of meromorphic functions sharing one value.
Uniqueness of meromorphic functions sharing three values
We prove a result on the uniqueness of meromorphic functions sharing three values with weights and as a consequence of this result we improve a recent result of W. R. Lü and H. X. Yi.
Uniqueness of meromorphic functions sharing three weighted values.
Uniqueness of meromorphic functions sharing values.
Uniqueness of meromorphic functions when two differential polynomials share one value IM
Uniqueness of meromorphic functions when two linear differential polynomials share the same 1-points
We prove a uniqueness theorem for meromorphic functions involving linear differential polynomials generated by them. As consequences of the main result we improve some previous results.
Uniqueness of meromorphic functions when two non-linear differential polynomials share a small function
In the paper we deal with the uniqueness of meromorphic functions when two non-linear differential polynomials generated by two meromorphic functions share a small function.
Uniqueness of nonlinear differential polynomials sharing simple and double 1-points.
Uniqueness of -shift difference polynomials of meromorphic functions sharing a small function
We investigate the uniqueness of a -shift difference polynomial of meromorphic functions sharing a small function which extend the results of N. V. Thin (2017) to -difference operators.
Uniqueness of transcendental meromorphic functions with their nonlinear differential polynomials sharing the small function.
Uniqueness of two analytic functions sharing four values in an angular domain
We deal with the uniqueness problem for analytic functions sharing four distinct values in an angular domain and obtain some theorems which improve the result given by Cao and Yi [J. Math. Anal. Appl. 358 (2009)].
Uniqueness results of meromorphic functions whose nonlinear differential polynomials have one nonzero pseudo value
Uniqueness theorems and normal families of entire functions and their derivatives
We use the theory of normal families to obtain some uniqueness theorems for entire functions, which improve and generalize the related results of Rubel and Yang, and Li and Yi. Some examples are provided to show the sharpness of our results.
Uniqueness theorems for entire functions whose difference polynomials share a meromorphic function of a smaller order
We deal with uniqueness of entire functions whose difference polynomials share a nonzero polynomial CM, which corresponds to Theorem 2 of I. Laine and C. C. Yang [Proc. Japan Acad. Ser. A 83 (2007), 148-151] and Theorem 1.2 of K. Liu and L. Z. Yang [Arch. Math. 92 (2009), 270-278]. We also deal with uniqueness of entire functions whose difference polynomials share a meromorphic function of a smaller order, improving Theorem 5 of J. L. Zhang [J. Math. Anal. Appl. 367 (2010), 401-408], where the entire...
Uniqueness theorems for meromorphic functions.
Uniqueness theorems for meromorphic functions concerning fixed points
This paper is devoted to the study of uniqueness of meromorphic functions sharing only one value or fixed points. We improve some related results due to J. L. Zhang [Comput. Math. Appl. 56 (2008), 3079-3087] and M. L. Fang [Comput. Math. Appl. 44 (2002), 823-831], and we supplement some results given by M. L. Fang and X. H. Hua [J. Nanjing Univ. Math. Biquart. 13 (1996), 44-48] and by C. C. Yang and X. H. Hua [Ann. Acad. Sci. Fenn. Math. 22 (1997), 395-406].
Uniqueness theorems for meromorphic functions that share three sets with weights.
Univalence of odd derivatives of even entire functions.
Univalent functions and Dirichlet integral.
Universal sequences for Zalcman’s Lemma and -normality
We prove the existence of sequences , ϱₙ → 0⁺, and , |zₙ| = 1/2, such that for every α ∈ ℝ and for every meromorphic function G(z) on ℂ, there exists a meromorphic function on ℂ such that converges to G(ζ) uniformly on compact subsets of ℂ in the spherical metric. As a result, we construct a family of functions meromorphic on the unit disk that is -normal for no m ≥ 1 and on which an extension of Zalcman’s Lemma holds.