On the Uniqueness of Certain Type of Shift Polynomial Sharing a Small Function

Sujoy Majumder

doi:10.1515/awutm-2017-0007

.blurhash-client-img { display: none !important; }

On the Uniqueness of Certain Type of Shift Polynomial Sharing a Small Function

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 55 (2017): Issue 1 (July 2017)

By: Sujoy Majumder

Open Access

|Sep 2017

Abstract

The purpose of the paper is to study the uniqueness problems of certain type of difference polynomial sharing a small function. We point out and rectify some gaps in the proof of the main results in [8]. In addition to this we obtain our main result as a corrected and generalized version of [8] in a more compact way which in turn improve a number of earlier results.

References

[1] S. S. Bhoosnurmath and S. R. Kabbur, Value distribution and uniqueness theorems for difference of entire and meromorphic function, Int. J. Anal. Appl., 2, ( 2013), 124-136.10.1155/2013/926340
Search in Google Scholar Back to article
[2] Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of f(z + ff) and difference equations in complex plane, Ramanujan J., 16, ( 2008), 105-129.10.1007/s11139-007-9101-1
Search in Google Scholar Back to article
[3] M. R. Chen and Z. X. Chen, Properties of difference polynomials of entire functions with finite order, Chinese Annals of Mathematics, 33A, ( 2012), 359-374.
Search in Google Scholar Back to article
[4] J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and J. L. Zhang, Value sharing results for shifts of meromorphic function, and sufficient conditions for periodicity, J. Math. Anal. Appl., 355, (2009), 352-363.10.1016/j.jmaa.2009.01.053
Search in Google Scholar Back to article
[5] W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964
Search in Google Scholar Back to article
[6] Value distribution of certain differential polynomials, Int. J. Math. Math. Sc., 28, ( 2001), 83-91.10.1155/S0161171201011036
Search in Google Scholar Back to article
[7] I. Lahiri,Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46, (2001), 241-253.10.1080/17476930108815411
Search in Google Scholar Back to article
[8] P. Sahoo and B. Saha, Value distribution and uniqueness of certain type of difference polynomials, Appl. Math. E-Notes, 16, (2016), 33-44.10.30755/NSJOM.03331
Search in Google Scholar Back to article
[9] X. G. Qi, L. Z. Yang, and K. Liu, Uniqueness and periodicity of meromorphic functions concerning the difference operator, Comput. Math. Appl., 60, ( 2010)), 1739-1746.10.1016/j.camwa.2010.07.004
Search in Google Scholar Back to article
[10] C. C. Yang, On deficiencies of differential polynomials II, Math. Z., 125, (1972), 107-112.10.1007/BF01110921
Search in Google Scholar Back to article
[11] K. Yamanoi, The second main theorem for small functions and related problems, Acta Math., 192, (2004), 225-29410.1007/BF02392741
Search in Google Scholar Back to article
[12] J. L. Zhang, Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., 367, (2010), 401-408.10.1016/j.jmaa.2010.01.038
Search in Google Scholar Back to article
[13] Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math., 6 (4), ( 2005), Art.116 [ ONLINE http://jipam.vu.edu.au/]
Search in Google Scholar Back to article