Generalized Relative Type and Generalized Weak Type of Entire Functions

Abstract

A single valued function of one complex variable which is analytic in the finite complex plane is called an integral (entire) function. For example exp 𝑧, sin𝑧, and cos𝑧 are examples of entire functions. In the value distribution theory one studies how an entire function assumes some values and the influence of assuming certain values in some specific manner on a function. In 1926 Rolf Nevanlinna initiated the value distribution theory of entire functions. This value distribution theory is a prominent branch of complex analysis and is the prime concern of the paper. Perhaps the Fundamental Theorem of Classical Algebra which states that “if 𝑓 is a polynomial of degree 𝑛 with real or complex coefficients, then the equation 𝑓(𝑧) = 0 has at least one root” is the most well known value distribution theorem.