GENERALISED ITERATION OF ENTIRE FUNCTIONS WITH INDEX-PAIR $[p,q]$
Year 2017,
Volume: 5 Issue: 1, 132 - 144, 01.04.2017
DIBYENDU Banerjee
,
BISWAJIT Mandal
Abstract
Using generalised iteration [2] of two entire functions we extend the results of Hong-Yan Xu et.al [16] for generalised iterated entire functions with index-pair $[p,q]$.
References
- [1] Banerjee, D. and Mandal, B., Generalised iteration of entire functions with nite iterated order, Journal of Classical Analysis, Vol:7, No:1 (2015), 47-62.
- [2] Banerjee, D. and Mondal, N., Maximum modulus and maximum term of generalized iterated entire functions, Bulletin of the Allahabad Mathematical Society, Vol:27, No:1 (2012), 117-131.
- [3] Bernal, L. G., On growth k-order of solutions of a complex homogeneous linear differential equations, Proc. Amer. Math. Soc., Vol:101, No:2 (1987), 317-322.
- [4] Clunie, J., The Composition of Entire and Meromorphic Functions, Mathematical Essays Dedicated to A. J. Macintyre, Ohio University Press, 1970, 75-92.
- [5] Hayman, W. K., Meromorphic Functions, Clarendon Press, Oxford, 1964.
- [6] Juneja, O. P., Kapoor, G. P. and Bajpai, S. K., On the (p,q)-order and lower (p,q)-order of an entire function, J. Reine Angew. Math., 282, (1976), 53-67.
- [7] Kinnunen, L., Linear differential equations with solutions of nite iterated order, Southeast Asian Bull. Math., Vol:22, No:4 (1998), 385-405.
- [8] 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.
- [9] Lahiri, I. and Sharma, D. K., On the growth of composite entire and meromorphic functions, Indian J. Pure Appl. Math., Vol:35, No:4 (2004), 525-543.
- [10] Niino, K. and Smita, N., Growth of a composite function of entire functions, Kodai Math. J., 3, (1980), 374-379.
- [11] Niino, K. and Yang, C.C., Some growth relationships on factors of two composite entire functions, in : Factorization Theory of Meromorphic Functions and Related Topics, Marcel Dekker Inc., New York/Basel, 1982, 95-99.
- [12] Sato, D., On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69, (1963), 411-414.
- [13] Singh, A. P., Growth of composite entire functions, Kodai Math. J., 8, (1985), 99-102.
- [14] Singh, A. P., On the maximum term of composite entire functions, Proc. Nat. Acad. India, 59, (1989), 103-115.
- [15] Tu, J., Chen, Z. X. and Zheng, X. M., Composition of entire functions with nite iterated order, J. Math. Anal. Appl., 353, (2009), 295-304.
- [16] Xu, H. Y., Tu, J. and Yi, C. F., The applications on some inequalities of the composition of entire functions, Journal of Mathematical Inequalities, Vol:7, No:4 (2013), 759-772.
- [17] Zhou, Z. Z., Growth of composite entire functions, Kodai Math. J., 9, (1986), 419-420.
Year 2017,
Volume: 5 Issue: 1, 132 - 144, 01.04.2017
DIBYENDU Banerjee
,
BISWAJIT Mandal
References
- [1] Banerjee, D. and Mandal, B., Generalised iteration of entire functions with nite iterated order, Journal of Classical Analysis, Vol:7, No:1 (2015), 47-62.
- [2] Banerjee, D. and Mondal, N., Maximum modulus and maximum term of generalized iterated entire functions, Bulletin of the Allahabad Mathematical Society, Vol:27, No:1 (2012), 117-131.
- [3] Bernal, L. G., On growth k-order of solutions of a complex homogeneous linear differential equations, Proc. Amer. Math. Soc., Vol:101, No:2 (1987), 317-322.
- [4] Clunie, J., The Composition of Entire and Meromorphic Functions, Mathematical Essays Dedicated to A. J. Macintyre, Ohio University Press, 1970, 75-92.
- [5] Hayman, W. K., Meromorphic Functions, Clarendon Press, Oxford, 1964.
- [6] Juneja, O. P., Kapoor, G. P. and Bajpai, S. K., On the (p,q)-order and lower (p,q)-order of an entire function, J. Reine Angew. Math., 282, (1976), 53-67.
- [7] Kinnunen, L., Linear differential equations with solutions of nite iterated order, Southeast Asian Bull. Math., Vol:22, No:4 (1998), 385-405.
- [8] 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.
- [9] Lahiri, I. and Sharma, D. K., On the growth of composite entire and meromorphic functions, Indian J. Pure Appl. Math., Vol:35, No:4 (2004), 525-543.
- [10] Niino, K. and Smita, N., Growth of a composite function of entire functions, Kodai Math. J., 3, (1980), 374-379.
- [11] Niino, K. and Yang, C.C., Some growth relationships on factors of two composite entire functions, in : Factorization Theory of Meromorphic Functions and Related Topics, Marcel Dekker Inc., New York/Basel, 1982, 95-99.
- [12] Sato, D., On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69, (1963), 411-414.
- [13] Singh, A. P., Growth of composite entire functions, Kodai Math. J., 8, (1985), 99-102.
- [14] Singh, A. P., On the maximum term of composite entire functions, Proc. Nat. Acad. India, 59, (1989), 103-115.
- [15] Tu, J., Chen, Z. X. and Zheng, X. M., Composition of entire functions with nite iterated order, J. Math. Anal. Appl., 353, (2009), 295-304.
- [16] Xu, H. Y., Tu, J. and Yi, C. F., The applications on some inequalities of the composition of entire functions, Journal of Mathematical Inequalities, Vol:7, No:4 (2013), 759-772.
- [17] Zhou, Z. Z., Growth of composite entire functions, Kodai Math. J., 9, (1986), 419-420.