Abstract: In 1998, several generalizations of uniform boundedness principle (U.B.P) was given for functions from topological spaces to topological spaces by Joseph, Kwack, and Nayar. Recently, using the definition of $u$-closure operator and $\alpha$-set, we introduced three classes of continuous functions, namely $\alpha$u-continuous, strongly u-continuous and semi-$\alpha$u-continuous functions. In this study the U.B.P. is extended using these generalized continuous functions.
Keywords: Uniform boundedness, Generalize continuous functions, Urysohn spaces.