COMPARATIVE GROWTH ESTIMATES OF DIFFERENTIAL MONOMIALS DEPENDING UPON THEIR RELATIVE ORDERS, RELATIVE TYPE AND RELATIVE WEAK TYPE
Year 2016,
Volume: 4 Issue: 2, 230 - 246, 01.10.2016
Sanjib Kumar Datta
Tanmay Bıswas
Abstract
In this paper the comparative growth properties of composition of entire and meromorphic functions on the basis of their relative orders (relative lower orders), relative types and relative weak types of di erential monomials generated by entire and meromorphic functions have been investigated.
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Year 2016,
Volume: 4 Issue: 2, 230 - 246, 01.10.2016
Sanjib Kumar Datta
Tanmay Bıswas
References
- [1] Bernal, L., Crecimiento relativo de funciones enteras. Contribucion al estudio de lasfunciones
enteras con ndice exponencialnito, Doctoral Dissertation, University of Seville, Spain, 1984.
- [2] Bernal, L., Orden relative de crecimiento de funciones enteras, Collect. Math., Vol:39 (1988),
209-229.
- [3] Bergweiler, W., On the Nevanlinna characteristic of a composite function, Complex Vari-
ables, Vol:10 (1988), 225-236.
- [4] Bergweiler, W., On the growth rate of composite meromorphic functions, Complex Variables,
Vol:14 (1990), 187-196.
- [5] Doeringer, W., Exceptional values of dierential polynomials, Pacic J. Math., Vol:98, No.1
(1982), 55-62.
- [6] Datta, S. K. and Biswas, T., On a result of Bergweiler, International Journal of Pure and
Applied Mathematics (IJPAM), Vol:51, No. 1 (2009), 33-37.
- [7] Datta, S. K. and Jha, A., On the weak type of meromorphic functions, Int. Math. Forum,
Vol:4, No.12 (2009), 569-579.
- [8] Datta, S. K. and Biswas, A., On relative type of entire and meromorphic functions, Advances
in Applied Mathematical Analysis, Vol:8, No.2 (2013),63-75.
- [9] Datta, S. K., Biswas, T. and Biswas, C., Measure of growth ratios of composite entire and
meromorphic functions with a focus on relative order, International J. of Math. Sci. & Engg.
Appls. (IJMSEA), Vol:8, No. IV (July, 2014), 207-218.
- [10] Datta, S. K., Biswas, T. and Bhattacharyya, S., On relative order and relative type based
growth properties of dierential monomials, Journal of the Indian Math. Soc., Vol. 82, Nos.
(3 - 4), (2015), pp. 39{52.
- [11] Hayman, W. K. Meromorphic Functions, The Clarendon Press, Oxford (1964).
- [12] Lahiri, I. and Sharma, D. K., Growth of composite entire and meromorphic functions, Indian
J. Pure Appl. Math., Vol:26, No.5 (1995), 451-458.
- [13] Lahiri, B. K. and Banerjee, D., Relative order of entire and meromorphic functions, Proc.
Nat. Acad. Sci. India Ser. A., Vol:69(A), No. 3 (1999), 339-354.
- [14] Roy, C., Some properties of entire functions in one and several complex vaiables, Ph.D.
Thesis ( 2010), University of Calcutta.
- [15] Valiron, G., Lectures on the general theory of integral functions, Chelsea Publishing Company,
1949.
- [16] Yang, L., Value distribution theory and new research on it, Science Press, Beijing (1982).
- [17] Yi, H. X., On a result of Singh, Bull. Austral. Math. Soc., Vol:41 (1990), 417-420.