You have just completed your registration at OpenAire.
Before you can login to the site, you will need to activate your account.
An e-mail will be sent to you with the proper instructions.
Important!
Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version
of the site upon release.
In this thesis, we mainly worked in the following areas: value distributions of meromorphic functions, normal families, Bank-Laine functions and complex oscillation theory. In the first chapter we will give an introduction to those areas and some related topics that are needed. In Chapter 2 we will prove that for a meromorphic function f and a positive integer k, the function af(f(k))n -1, n ≥ 2, has infinitely many zeros and then we will prove that it is still true when we replace f(k) by a differential polynomial. In Chapter 3 we will prove that for a merornorphic function f and a positive integer k, the function af f(k) -1 with N1(r, 1/f^((k)) ) = S(r, f) has infinitely many zeros and then we will prove that it is still true when we replace f(k) by a differential polynomial. In Chapter 4 we will apply Bloch's Principle to prove that a family of functions meromorphic on the unit disc B(0, 1), such that f(f1)m≠ 1, m ≠ 2, is normal. Also we will prove that a family of functions meromorphic on B(0,1), such that each f ≠ 0 and f(f(k))m ,k, m ∈N omits the value 1, is normal. In the fifth chapter we will generalise Theorem 5.1.1 for a sequence of distinct complex numbers instead of a sequence of real numbers. Also, we will get very nice new results on Bank-Laine functions and Bank-Laine sequences. In the last chapter we will work on the relationship between the order of growth of A and the exponent of convergence of the solutions y(k) +Ay =0, where A is a transcendental entire function with ρ(A) < 1/2.