The main purpose of this paper is to study the approximate best proximity pair of cyclic maps and their diameter in fuzzy normed spaces defined by Bag and Samanta. First, approximate best point proximity points on fuzzy normed linear spaces are defined and four general lemmas are given regarding approximate fixed point and approximate best proximity pair of cyclic maps on fuzzy normed spaces. U...

Over the last few decades, a certain interesting class of functional equations were developed while obtaining generating functions many system distributions. This has numerous applications in modern disciplines such as wireless networks and communications. The Ulam stability theorem can be applied to investigating when approximated Banach spaces, algebra, so on. main focus this study is analyse...

In this paper, the concept of fuzzy automata normed linear structure spaces is introduced and suitable examples are provided. ;The ;concepts of fuzzy automata $alpha$-open sphere, fuzzy automata $mathscr{N}$-locally compact spaces, fuzzy automata $mathscr{N}$-Hausdorff spaces are also discussed. Some properties related with to fuzzy automata normed linear structure spaces and fuzzy automata $ma...

A construction analogous to that of Godefroy–Kalton for metric spaces allows one embed isometrically, in a canonical way, every quasi-metric space $(X,d)$ an asymmetric normed $\mathcal {F}_a(X,d)$ (its free space, also called asy

It is well known that every normed (even quasibarrelled) space a Mackey space. However, in the more general realm of locally quasi-convex abelian groups an analogous result does not hold. We give first examples spaces which are groups.

in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.

In cite{p}, Park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}label{E01}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| \ && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|

n this paper we study the Hyers-Ulam-Rassias stability of Cauchyequation in Felbin's type fuzzy normed linear spaces. As a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in classical analysis. This shows how the category offuzzy normed linear spaces differs from the classical normed linearspac...