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 P, the concepts of P-bounded set and γ-maxpseudo-norm-subadditive operator in F ∗ space are introduced. The uniform boundedness princ...

In this article we deal with the Riemann integral of functions from R into a real Banach space. The last theorem establishes the integrability of continuous functions on the closed interval of reals. To prove the integrability we defined uniform continuity for functions from R into a real normed space, and proved related theorems. We also stated some properties of finite sequences of elements o...

In this article we deal with the Riemann integral of functions from R into a real Banach space. The last theorem establishes the integrability of continuous functions on the closed interval of reals. To prove the integrability we defined uniform continuity for functions from R into a real normed space, and proved related theorems. We also stated some properties of finite sequences of elements o...

In this paper, we consider the concepts co-farthest points innormed linear spaces. At first, we define farthest points, farthest orthogonalityin normed linear spaces. Then we define co-farthest points, co-remotal sets,co-uniquely sets and co-farthest maps. We shall prove some theorems aboutco-farthest points, co-remotal sets. We obtain a necessary and coecient conditions...

In this paper, we study the concept of statistical convergence on L?fuzzy normed spaces. Then give a useful characterization for statistically convergent sequences. Furthermore, illustrate that our method is more general than usual

In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R...