International Journal of Engineering, Science and Mathematics

  • Year: 2018
  • Volume: 7
  • Issue: 5

On some growth properties related to certain type of difference polynomials

  • Author:
  • Sanjib Kumar Datta1, Satavisha Dey2
  • Total Page Count: 12
  • DOI:
  • Page Number: 78 to 89

1Department of Mathematics, University of Kalyani P.O.-Kalyani, Dist.-Nadia, Pin-741235

2Department of Mathematics, Bijoy Krishna Girls’ College, M.G. Road, Howrah-711101

Abstract

For an entire function, we define the difference operators as Δcf(z)=f(z+c)-f(z) and Δncf(z)=ΔCn-1 (ΔcF(Z)) where is a non-zero complex number and n ≥ 2 being a positive integer. If c = 1 we write Δcf(z)=Δf(Z). Now let us consider, where f being an entire function n, m, yj(J=1, 2, 3,….d) and, are all non-negative integers. Then F is called the difference monomial generated by entire f. In this paper, we will establish some comparative growth properties of differential-difference polynomials of the above form generated by an entire function f as indicated. In fact, the results obtained here improve some earlier theorems.

Keywords

Transcendental entire function, difference polynomials, growth properties, unbounded function, order(lower order), Ψ-order(Ψlowerorder, type(lower type), Ψ-type(Ψ-lower type) maximum term