SOME RESULTS ON THE COMPARATIVE GROWTH ANALYSIS OF ENTIRE FUNCTIONS UNDER THE TREATMENT OF THEIR MAXIMUM TERMS AND GENERALIZED RELATIVE L* -ORDERS
Yıl 2017,
Cilt: 66 Sayı: 2, 162 - 174, 01.08.2017
Sanjıb Kumar Datta
Tanmay Bıswas
Öz
In this paper we estimate some comparative growth properties of composition of entire functions in terms of their maximum terms on the basis of their generalized relative L* order (respectively generalized relative L* lower order ) with respect to another entire function
Kaynakça
- Bernal, L., Orden relative de crecimiento de funciones enteras, Collect. Math., Vol. 39 (1988), pp. 209-229.
- Datta, S. K. and T. Biswas, Growth of entire functions based on relative order, International Journal of Pure and Applied Mathematics (IJPAM), Vol. 51, No. 1 (2009), pp.49-58.
- Datta, S. K. and A. R. Maji, Relative order of entire functions in terms of their maximum terms, Int. Journal of Math. Analysis, Vol. 5, No. 43 (2011), pp. 2119-2126.
- S. K. Datta, T. Biswas and S. Ali, Growth estinmates of composite entire functions based on maximum terms using their relative L-order, Advances in Applied Mathematical Analysis (AAMA), Vol.7, No. 2 (2012), pp. 119-134.
- Datta, S. K., T. Biswas and J. H. Shaikh, Computation on the comparative growth analy- sis of entire functions depending on their generalized relative orders, Functional Analysis, Approximation and Computation, Vol. 8, No. 1(2016), pp. 39-49.
- Datta, S. K., T. Biswas and A. Hoque, Some results on the growth analysis of entire functions using their maximum terms and relative L - orders, Journal of Mathematical Extension, Accepted for publication (2016) and to appear.
- Lahiri, B. K. and D. Banerjee, Generalised relative order of entire functions, Proc. Nat. Acad. Sci. India, Vol. 72(A), No. IV (2002), pp. 351-271.
- Singh, S. K. and G. P. Barker, Slow ly changing functions and their applications, Indian J. Math., Vol. 19, No. 1 (1977), pp 1-6.
- Somasundaram, D. and R. Thamizharasi, A note on the entire functions of L-bounded index and L-type, Indian J. Pure Appl. Math., Vol. 19, No. 3 ( March 1988) , pp. 284-293.
- Singh, A. P., On maximum term of composition of entire functions, Proc. Nat. Acad. Sci. India, Vol. 59(A), Part I(1989), pp. 103-115.
- Singh, A. P. and M. S. Baloria, On maximum modulus and maximum term of composition of entire functions, Indian J. Pure Appl. Math., Vol. 22, No. 12 (1991) , pp. 1019-1026.
- Titchmarsh, E.C., The theory of functions , 2nd ed. Oxford University Press, Oxford , 1968. [13] Valiron, G., Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949.
- Current address : Sanjib Kumar Datta: Department of Mathematics, University of Kalyani P.O.-Kalyani, Dist-Nadia, PIN- 741235, West Bengal, India.
- E-mail address : sanjib_kr_datta@yahoo.co.in
- Current address : Tanmay Biswas: Rajbari, Rabindrapalli, R. N. Tagore Road P.O.-Krishnagar, Dist-Nadia, PIN- 741101, West Bengal, India.
- E-mail address : tanmaybiswas_math@rediffmail.com
Yıl 2017,
Cilt: 66 Sayı: 2, 162 - 174, 01.08.2017
Sanjıb Kumar Datta
Tanmay Bıswas
Kaynakça
- Bernal, L., Orden relative de crecimiento de funciones enteras, Collect. Math., Vol. 39 (1988), pp. 209-229.
- Datta, S. K. and T. Biswas, Growth of entire functions based on relative order, International Journal of Pure and Applied Mathematics (IJPAM), Vol. 51, No. 1 (2009), pp.49-58.
- Datta, S. K. and A. R. Maji, Relative order of entire functions in terms of their maximum terms, Int. Journal of Math. Analysis, Vol. 5, No. 43 (2011), pp. 2119-2126.
- S. K. Datta, T. Biswas and S. Ali, Growth estinmates of composite entire functions based on maximum terms using their relative L-order, Advances in Applied Mathematical Analysis (AAMA), Vol.7, No. 2 (2012), pp. 119-134.
- Datta, S. K., T. Biswas and J. H. Shaikh, Computation on the comparative growth analy- sis of entire functions depending on their generalized relative orders, Functional Analysis, Approximation and Computation, Vol. 8, No. 1(2016), pp. 39-49.
- Datta, S. K., T. Biswas and A. Hoque, Some results on the growth analysis of entire functions using their maximum terms and relative L - orders, Journal of Mathematical Extension, Accepted for publication (2016) and to appear.
- Lahiri, B. K. and D. Banerjee, Generalised relative order of entire functions, Proc. Nat. Acad. Sci. India, Vol. 72(A), No. IV (2002), pp. 351-271.
- Singh, S. K. and G. P. Barker, Slow ly changing functions and their applications, Indian J. Math., Vol. 19, No. 1 (1977), pp 1-6.
- Somasundaram, D. and R. Thamizharasi, A note on the entire functions of L-bounded index and L-type, Indian J. Pure Appl. Math., Vol. 19, No. 3 ( March 1988) , pp. 284-293.
- Singh, A. P., On maximum term of composition of entire functions, Proc. Nat. Acad. Sci. India, Vol. 59(A), Part I(1989), pp. 103-115.
- Singh, A. P. and M. S. Baloria, On maximum modulus and maximum term of composition of entire functions, Indian J. Pure Appl. Math., Vol. 22, No. 12 (1991) , pp. 1019-1026.
- Titchmarsh, E.C., The theory of functions , 2nd ed. Oxford University Press, Oxford , 1968. [13] Valiron, G., Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949.
- Current address : Sanjib Kumar Datta: Department of Mathematics, University of Kalyani P.O.-Kalyani, Dist-Nadia, PIN- 741235, West Bengal, India.
- E-mail address : sanjib_kr_datta@yahoo.co.in
- Current address : Tanmay Biswas: Rajbari, Rabindrapalli, R. N. Tagore Road P.O.-Krishnagar, Dist-Nadia, PIN- 741101, West Bengal, India.
- E-mail address : tanmaybiswas_math@rediffmail.com