SOME RESULTS ON THE COMPARATIVE GROWTH ANALYSIS OF ENTIRE FUNCTIONS UNDER THE TREATMENT OF THEIR MAXIMUM TERMS AND GENERALIZED RELATIVE L* -ORDERS

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

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  • 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