Using the fixed point method, we establish a generalized Ulam Hyers stability result for the monomial functional equation in the setting of complete random p-normed spaces. As a particular case, we obtain a new stability theorem for monomial functional equations in β-normed spaces.

the notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $cat(0)$ space, where the curvature is bounded from above by zero. in fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. in this paper, w...

In this article, we formalize topological properties of real normed spaces. In the first few parts, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. In the middle of the article, we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, ima...

in this paper, we consider a generalization of the real normed spaces and give some examples.

In this work, our purpose is to introduce I−convergence of sequences of functions in intuitionistic fuzzy normed space by combining the I−convergence, the sequences of functions and the intuitionistic fuzzy normed spaces, and to investigate relations among concepts such as I−convergence, statistical convergence and the usual convergence of sequences of functions in intuitionistic fuzzy normed s...

in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real ...

we introduce some new concepts of topological spaces which say α − separable topologicalspace and o-topological group, α − first axiom, α − second axiom, and we find some relations betweenthem with some applications in normed spaces.

the goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--archimedean spacesand also in $p$--banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.