Browse > Article
http://dx.doi.org/10.11568/kjm.2019.27.4.899

SOME GROWTH ASPECTS OF SPECIAL TYPE OF DIFFERENTIAL POLYNOMIAL GENERATED BY ENTIRE AND MEROMORPHIC FUNCTIONS ON THE BASIS OF THEIR RELATIVE (p, q)-TH ORDERS  

Biswas, Tanmay
Publication Information
Korean Journal of Mathematics / v.27, no.4, 2019 , pp. 899-927 More about this Journal
Abstract
In this paper we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q)-th order and relative (p, q)-th lower order where p, q are any two positive integers and that of a special type of differential polynomial generated by one of the factors.
Keywords
Entire function; meromorphic function; index-pair; (p, q)-th order; relative (p, q)-th order; composition; growth; Property (A); special type of differential polynomial;
Citations & Related Records
연도 인용수 순위
  • Reference
1 L. Bernal-Gonzalez, Crecimiento relativo de funciones enteras. Aportaciones al estudio de las funciones enteras con indice exponencial finito, Doctoral Thesis, 1984, Universidad de Sevilla, Spain.
2 L. Bernal, Orden relative de crecimiento de funciones enteras , Collect. Math., 39 (1988), 209-229.
3 W. Bergweiler, On the Nevanlinna characteristic of a composite function, Complex Variables Theory Appl. 10 (2-3) (1988), 225-236.   DOI
4 W. Bergweiler, On the growth rate of composite meromorphic functions, Complex Variables Theory Appl. 14 (1-4) (1990), 187-196.   DOI
5 S. S. Bhooshnurmath and K. S. L. N. Prasad, The value distribution of some differental polynomials, Bull. Cal. Math. Soc 101 (1) (2009), 55-62.
6 L. Debnath, S. K. Datta, T. Biswas and A. Kar, Growth of meromorphic functions depending on (p,q)-th relative order, Facta Univ. Ser. Math. Inform. 31 (3) (2016), 691-705.
7 S. K. Datta, T. Biswas and C. Biswas, Measure of growth ratios of composite entire and meromorphic functions with a focus on relative order, Int. J. Math. Sci. Eng. Appl. 8 (IV) (July, 2014), 207-218.
8 W.K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
9 O. P. Juneja, G. P. Kapoor and S. K. Bajpai, On the (p,q)-order and lower (p,q)-order of an entire function, J. Reine Angew. Math., 282 (1976), 53-67.
10 O. P. Juneja, G. P. Kapoor and S. K. Bajpai, On the (p,q)-type and lower (p,q)-type of an entire function, J. Reine Angew. Math., 290 (1977), 180-190.
11 I. Laine, Nevanlinna Theory and Complex Differential Equations, De Gruyter, Berlin, 1993.
12 G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea Pub-lishing Company, (1949).
13 L. M. S. Ruiz, S. K. Datta, T. Biswas and G. K. Mondal, On the (p,q)-th relative order oriented growth properties of entire functions, Abstract and Applied Analysis, Vol.2014, Article ID 826137, 8 pages, http://dx.doi.org/10.1155/2014/826137.
14 X. Shen, J. Tu and H. Y. Xu, Complex oscillation of a second-order linear differential equation with entire coefficients of [p; q]-$\varphi$ order, Adv. Difference Equ. 2014,2014: 200, 14 pages, http://www.advancesindifferenceequations.com/content/2014/1/200.
15 D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc. 69 (1963), 411-414.   DOI
16 C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003.
17 L. Yang, Value distribution theory, Springer-Verlag, Berlin, 1993.