Paranormed Spaces Research Articles

On fuzzy paranormed spaces

It is well-known that Paranormed spaces have more general properties than normed spaces. Until recently, the concept of paranorm has not been considered with the set of fuzzy numbers and there are no studies in literatüre from this point of view. So, our main aim in this work is to apply this notion to the set of fuzzy numbers and give the new concepts of fuzzy paranorm and fuzzy paranormed space. In addition, we discuss in detail the statistical convergence and statistically Cauchy sequence in a fuzzy paranormed space.

Stability Results of Quadratic-Additive Functional Equation Based on Hyers Technique in Matrix Paranormed Spaces

In this work, we introduce a mixed type of quadratic-additive (QA) functional equation and obtain its general solution. The objective of this work is to investigate the Ulam–Hyers stability of this quadratic-additive (QA) functional equation in matrix paranormed spaces (briefly, MP spaces) using the Hyers method for the factor sum of norms.

A new paranormed series space using Euler totient means and some matrix transformations

Paranormed spaces are important as a generalization of the normed spaces in terms of having more general properties. The aim of this study is to introduce a new paranormed space $ \left\vert \phi _{z}\right\vert \left( p\right) $ over the paranormed space $ \ell \left( p\right) $ using Euler totient means, where $p=\left( p_{k}\right) $ is a bounded sequence of positive real numbers. Besides this, we investigate topological properties and compute the $ \alpha -,\beta -,$ and $\gamma $ duals of this paranormed space. Finally, we characterize the classes of infinite matrices $(\left\vert \phi_{z}\right\vert \left( p\right) ,\lambda )$ and $(\lambda ,\left\vert \phi_{z}\right\vert \left( p\right) ),$ where $\lambda $ is any given sequence space.

Generalized Statistical Convergence of Double Sequences in Paranormed Spaces

We introduce the notion of (λ, µ)-statistical convergence of double sequences in a setting of paranormed space and prove that every convergent sequence is (λ, µ)-statistically convergent but not conversely by supporting an illustrative example. We also define the notions of (λ, µ)-statistical Cauchy and strongly (λ, µ)p-summable double sequences in a paranormed space and obtain their relationship with (λ, µ)- statistical convergence.

General solution and stability of quattuorvigintic functional equation in matrix paranormed spaces

In this current work, we acquire the general solution and Hyers-Ulam stability for a new form of Quattuorvigintic functional equation in Matrix Paranormed Space by using the direct and fixed point methods.

Hyers-Ulam Stability of Cubic and Quartic Functional Equations in Matrix Paranormed Spaces

In this paper, we prove the Hyers-Ulam stability of the cubic and quartic functional equations in matrix paranormed spaces.

FUNCTIONAL INEQUALITIES IN PARANORMED SPACES

Abstract. In this paper, we investigate additive functional in-equalities in paranormed spaces. Furthermore, we prove the Hyers-Ulam stability of additive functional inequalities in paranormedspaces. 1. Introduction and preliminariesThe concept of statistical convergence for sequences of real numberswas introduced by Fast [3] and Steinhaus [26] independently and sincethen several generalizations and applications of this notion have beeninvestigated by various authors (see [5, 14, 16, 17, 25]). This notion wasdeflned in normed spaces by Kolk [15].We recall some basic facts concerning Fr¶ e chet spaces.Definition 1.1. [28] Let X be a vector space. A paranorm P : X ! [0 ;1 ) is a function on X such that(1) P (0) = 0;(2) P ( ix ) = P ( x ) ;(3) P ( x + y ) • P ( x )+ P ( y ) (triangle inequality)(4) If ft n g is a sequence of scalars with t n ! t and fx n g ‰ X with P ( x n ix ) ! 0, then P ( t n x n itx ) ! 0 (continuity of multiplication).The pair ( X;P ) is called a paranormed space if P

ON PARA-NORMED SPACE WITH FUZZY VARIABLES BASED ON EXPECTED VALUED OPERATOR

Fuzzy variables are functions from credibility spaces to the set of real numbers. The set of fuzzy variables is a linear space with the classic operations of addition and multiplication by numbers. Its subspace formed by fuzzy variables with finite pth absolute moments is showed to be a complete para-normed space. The concept of para-normed space is novel, and is an extension of normed space. It is seen that most properties of normed spaces hold in para-normed spaces. Also some useful inequalities in para-normed spaces are obtained.