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In this study polynomial approximation and characterizations were done for entire functions in specific Banach spaces (Hardy space, Bergman space, and B(p,q, ) space), over Jordan Domain then the coefficient characterizations of generalized order and generalized type of entire function of slow growth, in terms of approximation errors in the Banach spaces, and over Jordan domain were obtained.Further, the study was conducted using the exact polynomial approximations as used earlier but for the entire functions of two complex variables. Then the characterizations of order and type of whole functions of two complex variables in terms of approximation errors in Banach spaces, necessary and sufficient conditions for an entire function to have prescribed growth have been obtained in terms of approximation errors by using the L^p norm. The characterizations of order and type of whole functions of two complex variables when f is restricted to the domain D for 2 p were also obtained.