We introduce the operation L copulative with T,L to define PN space under T,L and establish some basic properties of probabilistic seminorms and norms under T,L Finally, we discuss so-called L-simple spaces.

In this paper, we study the concepts of lacunary statistical convergent and lacunary statistical Cauchy sequences in probabilistic normed spaces and prove some basic properties.

In this paper we study the concept of asymptotically double lacunary statistical convergent sequences in probabilistic normed spaces and prove some basic properties.

In this paper we study the concept of lacunary statistical convergent triple sequences in probabilistic normed spaces and prove some basic properties.

We prove a general Ulam-Hyers stability theorem for a nonlinear equation in probabilistic metric spaces, which is then used to obtain stability properties for different kinds of functional equations linear functional equations, generalized equation of the square root, spiral generalized gamma equations in random normed spaces. As direct and natural consequences of our results, we obtain general...

Some new concepts of generating spaces of quasi-norm family are introduced and their linear topological structures are studied. These spaces are not necessarily locally convex. By virtue of some properties in these spaces, several Schauder-type fixed point theorems are proved, which include the corresponding theorems in locally convex spaces as their special cases. As applications, some new fix...