Research of complex functional equations by means of theory of meromorphic functions

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We are concerned with meromorphic solutions of some functional equations in the complex plane. We obtained a relation between difference Riccati equations and linear difference equations of second order, and also investigated the existence of meromorphic solutions to some functional equations and the order of growth of meromorphic solutions. Further, we considered the properties of meromorphic functions of small order. The general form of the Valiron-Mokhon’ko theorem is established. We applied this result to Schroder type functional equations. The relation between the coefficients of an entire function and the order of growth is obtained in order to investigate the existence of entire solution of linear q-difference equations.