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GENERALISED ITERATION OF ENTIRE FUNCTIONS WITH INDEX-PAIR $[p,q]$

Year 2017, Volume: 5 Issue: 1, 132 - 144, 01.04.2017

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

Abstract

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.
There are 17 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

DIBYENDU Banerjee

BISWAJIT Mandal This is me

Publication Date April 1, 2017
Submission Date February 19, 2017
Acceptance Date February 6, 2017
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Banerjee, D., & Mandal, B. (2017). GENERALISED ITERATION OF ENTIRE FUNCTIONS WITH INDEX-PAIR $[p,q]$. Konuralp Journal of Mathematics, 5(1), 132-144.
AMA Banerjee D, Mandal B. GENERALISED ITERATION OF ENTIRE FUNCTIONS WITH INDEX-PAIR $[p,q]$. Konuralp J. Math. April 2017;5(1):132-144.
Chicago Banerjee, DIBYENDU, and BISWAJIT Mandal. “GENERALISED ITERATION OF ENTIRE FUNCTIONS WITH INDEX-PAIR $[p,q]$”. Konuralp Journal of Mathematics 5, no. 1 (April 2017): 132-44.
EndNote Banerjee D, Mandal B (April 1, 2017) GENERALISED ITERATION OF ENTIRE FUNCTIONS WITH INDEX-PAIR $[p,q]$. Konuralp Journal of Mathematics 5 1 132–144.
IEEE D. Banerjee and B. Mandal, “GENERALISED ITERATION OF ENTIRE FUNCTIONS WITH INDEX-PAIR $[p,q]$”, Konuralp J. Math., vol. 5, no. 1, pp. 132–144, 2017.
ISNAD Banerjee, DIBYENDU - Mandal, BISWAJIT. “GENERALISED ITERATION OF ENTIRE FUNCTIONS WITH INDEX-PAIR $[p,q]$”. Konuralp Journal of Mathematics 5/1 (April 2017), 132-144.
JAMA Banerjee D, Mandal B. GENERALISED ITERATION OF ENTIRE FUNCTIONS WITH INDEX-PAIR $[p,q]$. Konuralp J. Math. 2017;5:132–144.
MLA Banerjee, DIBYENDU and BISWAJIT Mandal. “GENERALISED ITERATION OF ENTIRE FUNCTIONS WITH INDEX-PAIR $[p,q]$”. Konuralp Journal of Mathematics, vol. 5, no. 1, 2017, pp. 132-44.
Vancouver Banerjee D, Mandal B. GENERALISED ITERATION OF ENTIRE FUNCTIONS WITH INDEX-PAIR $[p,q]$. Konuralp J. Math. 2017;5(1):132-44.
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