let f, g and h be all entire functions of several complex variables. in this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.

We study the Lüroth problem for partial differential fields. The main result is following analog of generalized Lüroth's theorem: Let F be a field characteristic 0 with m commuting derivation operators, u=u1,…,un set indeterminates over F. prove that an intermediate G between and F〈u〉 simple extension if only dimension polynomial u form ωu/G(t)=n(t+mm)−(t+m−sm) some s∈N. This generalizes classi...

Our aim in this paper is to introduce some idea about generalized relative Nevanlinna order (α,β) and type of an analytic function with respect another the unit disc where α β are continuous non-negative functions on (-∞,+∞). So we discuss growth properties relating composition two basis as compared their corresponding left right factors.

In the paper we wish to establish some comparative growth properties of composite entire or meromorphic functions on the basis of generalized relative L∗-order and generalized relative L∗-lower order.

In the 1920’s, Ritt studied the operation of functional composition g ◦ h(x) = g(h(x)) on complex rational functions. In the case of polynomials, he described all the ways in which a polynomial can have multiple ‘prime factorizations’ with respect to this operation. Despite significant effort by Ritt and others, little progress has been made towards solving the analogous problem for rational fu...