The main purpose of this paper is to study the existence of afixed point in locally convex topology generated by fuzzy n-normed spaces.We prove our main results, a fixed point theorem for a self mapping and acommon xed point theorem for a pair of weakly compatible mappings inlocally convex topology generated by fuzzy n-normed spaces. Also we givesome remarks in locally convex topology generate...

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm that is itself locally uniformly convex.

a normed space $mathfrak{x}$ is said to have the fixed point property, if for each nonexpansive mapping $t : e longrightarrow e $ on a nonempty bounded closed convex subset $ e $ of $ mathfrak{x} $ has a fixed point. in this paper, we first show that if $ x $ is a locally compact hausdorff space then the following are equivalent: (i) $x$ is infinite set, (ii) $c_0(x)$ is infinite dimensional, (...

It is proved that there exist complemented subspaces of countable topo-logical products (locally convex direct sums) of Banach spaces which cannot be represented as topological products (locally convex direct sums) of Banach spaces The problem of description of complemented subspaces of a given locally convex space is one of the general problems of structure theory of locally convex spaces. In ...

We prove that the torsion of any closed space curve which bounds a simply connected locally convex surface vanishes at least 4 times. This answers a question of Rosenberg related to a problem of Yau on characterizing the boundary of positively curved disks in Euclidean space. Furthermore, our result generalizes the 4 vertex theorem of Sedykh for convex space curves, and thus constitutes a far r...

Given a class $${{\mathcal {P}}}$$ of Banach spaces, locally convex space (LCS) E is called multi- if can be isomorphically embedded into product spaces that belong to . We investigate the question whether free L(X) strongly nuclear, Schwartz, multi-Hilbert or multi-reflexive. If X Tychonoff containing an infinite compact subset then, as it follows from results Außenhofer (Topol Appl 134:90–102...

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...