• Title/Summary/Keyword: meromorphic functions

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COEFFICIENT BOUNDS FOR CERTAIN SUBCLASSES OF MEROMORPHIC AND BI-UNIVALENT FUNCTIONS

  • Panigrahi, Trailokya
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.5
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    • pp.1531-1538
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    • 2013
  • In the present investigation, the author introduces two interesting subclasses of normalized meromorphic univalent functions $w=f(z)$ defined on $\tilde{\Delta}:=\{z{\in}\mathbb{C}:1<{\mid}z{\mid}<{\infty}\}$ whose inverse $f^{-1}(w)$ is also univalent meromorphic in $\tilde{\Delta}$. Estimates for the initial coefficients are obtained for the functions in these new subclasses.

CERTAIN SUBCLASS OF STRONGLY MEROMORPHIC CLOSE-TO-CONVEX FUNCTIONS

  • Gagandeep Singh;Gurcharanjit Singh; Navyodh Singh
    • Korean Journal of Mathematics
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    • v.32 no.1
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    • pp.73-82
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    • 2024
  • The purpose of this paper is to introduce a new subclass of strongly meromorphic close-to-convex functions by subordinating to generalized Janowski function. We investigate several properties for this class such as coefficient estimates, inclusion relationship, distortion property, argument property and radius of meromorphic convexity. Various earlier known results follow as particular cases.

MEROMORPHIC FUNCTIONS SHARING FOUR VALUES WITH THEIR DIFFERENCE OPERATORS OR SHIFTS

  • Li, Xiao-Min;Yi, Hong-Xun
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1213-1235
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    • 2016
  • We prove a uniqueness theorem of nonconstant meromorphic functions sharing three distinct values IM and a fourth value CM with their shifts, and prove a uniqueness theorem of nonconstant entire functions sharing two distinct small functions IM with their shifts, which respectively improve Corollary 3.3(a) and Corollary 2.2(a) from [12], where the meromorphic functions and the entire functions are of hyper order less than 1. An example is provided to show that the above results are the best possible. We also prove two uniqueness theorems of nonconstant meromorphic functions sharing four distinct values with their difference operators.

COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASS OF MEROMORPHIC AND BI-UNIVALENT FUNCTIONS

  • Salehian, Safa;Zireh, Ahmad
    • Communications of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.389-397
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    • 2017
  • In this paper, we introduce and investigate an interesting subclass of meromorphic bi-univalent functions defined on ${\Delta}=\{z{\in}{\mathbb{C}}$ : 1 < |z| < ${\infty}\}$. For functions belonging to this class, estimates on the initial coefficients are obtained. The results presented in this paper would generalize and improve some recent works of several earlier authors.

ON PARTIAL VALUE SHARING RESULTS OF MEROMORPHIC FUNCTIONS WITH THEIR SHIFTS AND ITS APPLICATIONS

  • Noulorvang, Vangty;Pham, Duc Thoan
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.5
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    • pp.1083-1094
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    • 2020
  • In this paper, we give some uniqueness theorems of nonconstant meromorphic functions of hyper-order less than one sharing partially three or four small periodic functions with their shifts. As an application, some sufficient conditions for periodicity of meromorphic functions are given. Our results improve and extend previous results of W. Lin, X. Lin and A. Wu [11].