The purpose of this paper is to characterize the Banach spaces and the locally convex spaces E for which bounded additive measures or bounded σadditive measures with values in L(E, F ), the space of continuous linear maps from E into F , are of bounded semi-variation for any Banach space or locally convex space F . This paper gives an answer to a problem posed by D.H. Tucker in [6].

In this paper, we obtain bounded criteria on certain weighted Morrey spaces for the commutators generalized by some sublinear integral operators and weighted Lipschitz functions. We also present bounded criteria for commutators generalized by such sublinear integral operators and weighted BMO function on the weighted Morrey spaces. As applications, our results yield the same bounded criteria fo...

In this paper we study generalized symmetric Berwald spaces. We show that if a Berwald space $(M,F)$ admits a parallel $s-$structure then it is locally symmetric. For a complete Berwald space which admits a parallel s-structure we show that if the flag curvature of $(M,F)$ is everywhere nonzero, then $F$ is Riemannian.

In this paper, a new definition of locally convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of locally convex L-topological vector spaces given by Yan and Fang in 1999 is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced. By using a family of generalized L-fuzzy semi-norms, a characterization o...

‎The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$‎ ‎for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$‎, ‎where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself‎. Here the Caputo fractional derivative $D^{q}_c$ is used i...