Since modulus of convexity and generalized convexity mold has dual relationship

and generalized convexity mold has many excellent properties

in order to investigate whether there is a mold has dual nature with generalized modulus of convexity

if there is such a mold

then what properties the mold has. Author constructed the mold which has the dual nature with generalized modulus of convexity to start to find the generalized form smooth mold by applying Hahn-Banach theorem

and the corresponding definitions. After the given definition

the author proves as smooth mold generalized form of generalized modulus of smoothness

it can accurately portray the uniform smoothness of Banach space. Then we study monotonic

parity of modulus of generalized smoothness and other properties. Finally as an application for a Banach space has been a sufficient condition for the uniform formal structure of the generalized modulus of smoothness portrayed.