the main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. we develop the theory of t-bestsimultaneous approximation in quotient spaces. then, we discuss the relationshipin t-proximinality and t-chebyshevity of a given space and its quotientspace.

In this paper, we have generalized the definition of vector space by considering the group as a canonical $m$-ary hypergroup, the field as a krasner $(m,n)$-hyperfield and considering the multiplication structure of a vector by a scalar as hyperstructure. Also we will be consider a normed $m$-ary hypervector space and introduce the concept of convergence of sequence on $m$-ary hypernormed space...

In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuz...

Ehrhard, Pagani and Tasson proposed a model of probabilistic functional programming in category normed positive cones stable measurable cone maps, which can be seen as coordinate-free generalization coherence spaces. However, unlike the case spaces, it remained unclear if could refined to classical linear logic. In this work we consider somewhat similar gives indeed full propositional logic wit...

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...

a mapping $f:v^n longrightarrow w$, where $v$ is a commutative semigroup, $w$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. in this paper we prove the hyers-ulam stability of multi-additive mappings in 2-banach spaces. the corollaries from our main results correct some outcomes from [w.-g. park, approximate additive mappings i...

in this paper, we prove the hyers-ulam stability of the symmetric functionalequation $f(ph_1(x,y))=ph_2(f(x), f(y))$ in random normed spaces. as a consequence, weobtain some random stability results in the sense of hyers-ulam-rassias.