%0 Journal Article %T The uniform boundedness principles for \(\gamma\)-max-pseudo-norm-subadditive and quasi-homogeneous operators in \(F^*\) spaces %A Song, Ming-liang %J Journal of Nonlinear Sciences and Applications %D 2015 %V 8 %N 5 %@ ISSN 2008-1901 %F Song2015 %X In this paper, we prove that every \(F^*\) space (i.e., Hausdorff topological vector space satisfying the first countable axiom) can be characterized by means of its “standard generating family of pseudo-norms”. By using the standard generating family of pseudo-norms \(\mathcal{P}\), the concepts of \(\mathcal{P}\)-bounded set and \(\gamma\)-maxpseudo- norm-subadditive operator in \(F^*\) space are introduced. The uniform boundedness principles for family of \(\gamma\)-max-pseudo-norm-subadditive and quasi-homogeneous operators in \(F^*\) spaces are established. As applications, we obtain the corresponding uniform boundedness principles in classical normed spaces and Menger probabilistic normed spaces. %9 journal article %R 10.22436/jnsa.008.05.09 %U http://dx.doi.org/10.22436/jnsa.008.05.09 %P 540--556