Article
Licensed
Unlicensed Requires Authentication

Uniqueness properties of meromorphic functions in the light of three shared sets

  • EMAIL logo and
Published/Copyright: May 18, 2018
Become an author with De Gruyter Brill
Author Information Explore this Subject
Mathematica Slovaca
From the journal Mathematica Slovaca Volume 68 Issue 3

Abstract

We use the notion of weighted sharing of sets to improve a number of results in the uniqueness theory of meromorphic functions sharing three sets. We have also presented a new idea in the formation of one of the range sets in connection with the three shared set problems, which ultimately yields a better result than many existing result in some sense.

MSC 2010: Primary 30D35
Keywords: meromorphic functions; uniqueness; weighted sharing; shared sets

This research work is supported by the Council Of Scientific and Industrial Research, Extramural Research Division, CSIR Complex, Pusa, New Delhi-110012, India, under the sanction project no. 25(0229)/14/EMR-II.

Communicated by Stanisława Kanas

References

[1] Alzahary, T. C.: Meromorphic functions with weighted sharing of one set, Kyungpook Math. J. 47 (2007), 57–68.Search in Google Scholar

[2] Alzahary, T. C.—Yi, H. X.: Weighted value sharing and a question of I. Lahiri, Complex Var. Theory Appl. 49 (2004), 1063–1078.10.1080/02781070410001701074Search in Google Scholar

[3] Banerjee, A.—Bhattacharajee, P.: Uniqueness and set sharing of derivatives of meromorphic functions, Math. Slovaca. 61 (2011), 197–214.10.2478/s12175-011-0005-6Search in Google Scholar

[4] Banerjee, A.—Mallick, S.: On the bi-unique range sets for derivatives of meromorphic functions, Surv. Math. Appl. 10 (2015), 95–111.Search in Google Scholar

[5] Banerjee, A.—Mallick, S.: On the characterisations of a new class of strong uniqueness polynomials generating unique range sets, Comput. Methods Funct. Theory, 10.1007/s40315-016-0174-y.Search in Google Scholar

[6] Gross, F.: Factorization of meromorphic functions and some open problems. In: Proc. Conf. Univ. Kentucky, Leixngton, Ky(1976); Lecture Notes in Math. 599, Springer (Berlin), 1977, pp. 51–69.Search in Google Scholar

[7] Hayman, W. K.: Meromorphic Functions, The Clarendon Press, Oxford, 1964.Search in Google Scholar

[8] Lahiri, I.: Value distribution of certain differential polynomials, Int. J. Math. Math. Sci. 28 (2001), 83–91.10.1155/S0161171201011036Search in Google Scholar

[9] Lahiri, I.: Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193–206.10.1017/S0027763000027215Search in Google Scholar

[10] Lahiri, I.: Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl. 46 (2001), 241–253.10.1080/17476930108815411Search in Google Scholar

[11] Lahiri, I.—Banerjee, A.: Weighted sharing of two sets, Kyungpook Math. J. 46 (2006), 79–87.Search in Google Scholar

[12] Lin, W. C.—Yi, H. X.: Uniqueness theorems for meromorphic functions that share three sets, Complex Var. Theory Appl. 48 (2003), 315–327.10.1080/0278107021000037075Search in Google Scholar

[13] Mokhonko, A. Z.: On the Nevanlinna characteristics of some meromorphic functions. In: “Theory of functions, functional analysis and their applications”, Izd-vo Khar’kovsk, Un-ta. 14 (1971), 83–87.Search in Google Scholar

[14] Wu, A. D.—Lin, W. C.: Some properties of meromorphic functions concerning shared-sets, J. Classical Anal. 7 (2015), 1–15.10.7153/jca-07-01Search in Google Scholar

[15] Yi, H. X.: Uniqueness of meromorphic functions and a question of Gross, Sci. China Ser: A. 37 (1994), 802–813.Search in Google Scholar

[16] Yi, H. X.: Meromorphic functions that share one or two values II, Kodai Math. J. 22 (1999), 264–272.10.2996/kmj/1138044046Search in Google Scholar

Received: 2016-3-5
Accepted: 2017-1-14
Published Online: 2018-5-18
Published in Print: 2018-6-26

© 2018 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  2. Small-large subgroups of the reals
  4. Structural properties of algebras of S-probabilities
  6. Approximation in quantum measure spaces
  8. On Fibonomial sums identities with special sign functions: analytically q-calculus approach
  10. On the proximity of multiplicative functions to the number of distinct prime factors function
  12. Truncated euler polynomials
  14. Growth series of crossed and two-sided crossed products of cyclic groups
  16. Weakly U-abundant semigroups with strong Ehresmann transversals
  18. Iterative learning control with pulse compensation for fractional differential systems
  20. Rectifiable and nonrectifiable solution curves of half-linear differential systems
  22. Uniqueness properties of meromorphic functions in the light of three shared sets
  24. A new family of analytic functions defined by means of Rodrigues type formula
  26. Perturbation analysis of a nonlinear equation arising in the Schaefer-Schwartz model of interest rates
  28. On the solutions of a second-order difference equation in terms of generalized Padovan sequences
  30. Fixed points in C∗-algebra valued b-metric spaces endowed with a graph
  32. A general fixed point theorem for two pairs of mappings satisfying a mixed implicit relation
  34. Productively sequential spaces
  36. Euler classes of vector bundles over iterated suspensions of real projective spaces
  38. The stationary distribution and ergodicity of a stochastic mutualism model
  40. Restricted injective dimensions over local homomorphisms
https://doi.org/10.1515/ms-2017-0127
Keywords for this article
meromorphic functions; uniqueness; weighted sharing; shared sets

Articles in the same Issue

  2. Small-large subgroups of the reals
  4. Structural properties of algebras of S-probabilities
  6. Approximation in quantum measure spaces
  8. On Fibonomial sums identities with special sign functions: analytically q-calculus approach
  10. On the proximity of multiplicative functions to the number of distinct prime factors function
  12. Truncated euler polynomials
  14. Growth series of crossed and two-sided crossed products of cyclic groups
  16. Weakly U-abundant semigroups with strong Ehresmann transversals
  18. Iterative learning control with pulse compensation for fractional differential systems
  20. Rectifiable and nonrectifiable solution curves of half-linear differential systems
  22. Uniqueness properties of meromorphic functions in the light of three shared sets
  24. A new family of analytic functions defined by means of Rodrigues type formula
  26. Perturbation analysis of a nonlinear equation arising in the Schaefer-Schwartz model of interest rates
  28. On the solutions of a second-order difference equation in terms of generalized Padovan sequences
  30. Fixed points in C∗-algebra valued b-metric spaces endowed with a graph
  32. A general fixed point theorem for two pairs of mappings satisfying a mixed implicit relation
  34. Productively sequential spaces
  36. Euler classes of vector bundles over iterated suspensions of real projective spaces
  38. The stationary distribution and ergodicity of a stochastic mutualism model
  40. Restricted injective dimensions over local homomorphisms
Downloaded on 13.4.2026 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2017-0127/html
Scroll to top button