Korean J. Math. Vol. 27 No. 4 (2019) pp.899-927
DOI: https://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 $\left( p,q\right) $-th orders

Article Sidebar

PDF
Published: Dec 30, 2019
Keywords:
Entire function, meromorphic function, index-pair, $\left( p, q\right) $-th order, relative $% \left( p, composition, growth, Property (A), special type of differential polynomial.
Mathematics Subject Classification:
30D20, 30D30, 30D35

Main Article Content

Tanmay Biswas
Independent Researcher West Bengal, India..

Abstract

In this paper we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using relative $\left( p,q\right) $-th order and relative $\left( p,q\right) $-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.


Article Details

References

[1] L. Bernal-Gonzal ez, Crecimiento relativo de funciones enteras. Aportaciones al estudio de las funciones enteras con indice exponencial finito, Doctoral Thesis, 1984, Universidad de Sevilla, Spain. Google Scholar

[2] L. Bernal, Orden relative de crecimiento de funciones enteras , Collect. Math., 39 (1988), 209–229. Google Scholar

[3] W. Bergweiler, On the Nevanlinna characteristic of a composite function, Complex Variables Theory Appl. 10 (2-3) (1988), 225–236. Google Scholar

[4] W. Bergweiler, On the growth rate of composite meromorphic functions, Complex Variables Theory Appl. 14 (1-4) (1990), 187–196. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[8] W.K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964). Google Scholar

[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. Google Scholar

[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. Google Scholar

[11] I. Laine, Nevanlinna Theory and Complex Differential Equations, De Gruyter, Berlin, 1993. Google Scholar

[12] 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, Ab- stract and Applied Analysis, Vol.2014, Article ID 826137, 8 pages, http://dx.doi.org/10.1155/2014/826137. Google Scholar

[13] X. Shen, J. Tu and H. Y. Xu, Complex oscillation of a second-order linear differential equation with entire coefficients of [p, q] − φ order, Adv. Difference Equ. 2014,2014: 200, 14 pages, http://www.advancesindifferenceequations.com/content/2014/1/200. Google Scholar

[14] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc. 69 (1963), 411–414. Google Scholar

[15] C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dor- drecht, 2003. Google Scholar

[16] L. Yang, Value distribution theory, Springer-Verlag, Berlin, 1993. Google Scholar

[17] G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, (1949). Google Scholar