Abstract
In this paper, we investigate analogous of Milloux inequality and Hayman’s alternative for E-valued meromorphic functions from the complex plane ℂ to an infinite dimensional complex Banach space E with a Schauder basis. As an application of our results, we deduce some interesting analogous results for E-valued meromorphic functions from the complex plane ℂ to an infinite dimensional complex Banach space E with a Schauder basis. And also we have given the applications of homogeneous differential polynomials to the Nevanlinna’s theory of E-valued meromorphic functions from the complex plane ℂ to an infinite dimensional complex Banach space E with a Schauder basis and given some generalizations by these polynomials.
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