On The Research Of Meromorphic Solutions Of Functional Equations And Related Problem

The mapping t: N→N,defined , f or n∈ N , byThe iterates of this mapping are defined recursively byLet M be the set of all these numbers v∈N, (?)_m∈N, t_m(v)≠1, andt₀(n)= n, t_m(n) = t(t_m-(n)), n,m∈N.In 1994, L. Berg and G. Meinardus proved that: Function ( * ) is holomorphic solution ofin |z|<1. They conjecture that h(z) = C₀ + C₁(z/(1-z)), where λ = e^(2Ï€i)/3 , C₀,C₁ are constant.In this thesis, our main results is stated as following:Theorem 1 IF function ( * ) is meromorphic solution of ( * * ) in C,then h(z) =where z_j (j=l, 2, ... , k) are the poles of h(z) in C, A_j (j=l, 2, ..., k) are nonzero constant ,and c is the constant.If we can prove k = 1 and h(z) analytic continuation to C along z =1,...