Further Extending Results of Some Classes of Complex Difference and Functional Equations

The main purpose of this paper is to present some properties of the meromorphic solutions of complex difference equation of the form ∑ λ∈I αλ z ∏n ν 1f z cν lλ,ν / ∑ μ∈J βμ z ∏n ν 1f z cν mμ,ν R z, f z , where I {λ lλ,1, lλ,2, . . . , lλ,n | lλ,ν ∈ N ∪ {0}, ν 1, 2, . . . , n} and J {μ mμ,1,mμ,2, . . . , mμ,n | mμ, ν ∈ N ∪ {0}, ν 1, 2, . . . , n} are two finite index sets, cν ν 1, 2, . . . , n are distinct, nonzero complex numbers, αλ z λ ∈ I and βμ z μ ∈ J are small functions relative to f z , R z, f z is a rational function in f z with coefficients which are small functions of f z . We also consider related complex functional equations in the paper.