N-normed Spaces Research Articles

A Study of Boundedness in rectangular fuzzy n-normed spaces

A Study of Boundedness in rectangular fuzzy n-normed spaces

On (φ,ψ)-generalized weak contractions in quasi- normed spaces

We propose the definition of quasi-n-normed spaces and prove some new results on fixed points theory related to weak contractions in this framework. We prove the existence and uniqueness of fixed point for (φ,ψ)-generalized weak contractions and (φ,ψ)-generalized weak C-contractions in quasi n-normed spaces. The obtained results extend some known theorems for nonlinear contractive functions on quasi n-normed spaces. In addition, we demonstrate an application of obtained results to Integral Equation.

Rough Convergence of Double Sequences in $n-$Normed Spaces

In this study, we introduced the concepts of rough convergence, rough Cauchy double sequence, and the set of rough limit points of a double sequence, as well as the rough convergence criteria associated with this set in $n$-normed spaces. Later, we proved that this set is both closed and convex. Finally, we presented the relationships between rough convergence and rough Cauchy double sequence in $n$-normed spaces.

A New Notion of Inner Product in A Subspace of n-Normed Spaces

Given an n-normed space X for n>= 2$, we investigate the completness of Y (as subspace of X) respect to a new norm that corresponds this new inner product on Y. Moreover, we discuss the angle between two subspaces in Y.

Certain aspects of rough I-statistical convergence in probabilistic n-normed space

The main aim of this investigation is to introduce rough I-statistical convergence in probabilistic n-normed spaces (briefly Pr-n-spaces). We establish some results on roughI-statistical convergence and also we introduce the notion of rough I-statistical limit set in Pr-n-spaces and discuss some topological aspects on this set. Moreover, we define rough I-lacunary statistical convergent, rough lacunary I-convergent, rough lacunary I-Cauchy and rough lacunary I?-convergent sequences in Pr-n-spaces. We obtain several significant results related to these notions.

A new type of difference I-convergent sequence in IFnNS

In this paper, we introduce the notion of a generalized difference I-convergent (i.e.?m-I-convergent) and difference I-Cauchy (i.e.?m-I-Cauchy) sequence in intuitionistic fuzzy n-normed spaces. Further, we prove some results related to this notion. Also, we study the concepts of a generalized difference I*-convergent (i.e.?m-I*-convergent) sequence in intuitionistic fuzzy n-normed spaces and show the relation between them.

On <img src=image/13427444_01.gif>-Ideal Statistically Convergent of Double Sequences in n-Normed Spaces over Non-Archimedean Fields

The main aim of this work is to investigate some important properties of statistical convergence sequence in non-Archimedean fields. Statistical convergence has been discussed in various fields of mathematics namely approximation theory, measure theory, probability theory, trigonometric series, number theory, etc. The concept of summability over valued fields is a significant area of mathematics that has many applications in analytic continuation, quantum mechanics, probability theory, Fourier analysis, approximation theory, and fixed point theory. The theory of statistical convergence plays a notable space in the summability theory and functional analysis. The purpose of this work is to provide certain characterizations of <img src=image/13427444_01.gif> ideal statistical convergence of sequence and <img src=image/13427444_01.gif> ideal statistical Cauchy sequence in n-normed spaces and the establishment of relevant results in non-Archimedean fields. The <img src=image/13427444_01.gif> ideal statistical convergence of sequence and <img src=image/13427444_01.gif> ideal statistically Cauchy sequence are defined. A few related theorems are proved in field <img src=image/13427444_02.gif>. The results of this work are extended to establish statistical convergence of double sequences in n-normed space and some new results have been proved. In this work, the main concept is <img src=image/13427444_01.gif> ideal statistical convergence of double sequences in n-normed space over a complete, non-trivially valued, non-Archimedean field. Throughout this article, <img src=image/13427444_02.gif> is a complete, non-trivially valued, non-Archimedean field.

Orlicz-lacunary convergent triple sequences and ideal convergence

In the present paper we introduce and study Orlicz lacunary convergent triple sequences over n-normed spaces. We make an effort to present the notion of $g_{3}$-ideal convergence in triple sequence spaces. We examine some topological and algebraic features of new formed sequence spaces. Some inclusion relations are obtained in this paper. Finally, we investigate ideal convergence in these spaces.

SOME NEW BIQUADRATIC SEQUENCE SPACES OVER n-NORMED SPACES DEFINED BY MUSIELAK-ORLICZ FUNCTION

In this paper, we construct some new biquadratic sequence spaces using orlicz function defined by Musielak-Orlicz over n-normed spaces. We study some topological properties and inclusion relations between these spaces.

Some new sequence spaces in n-normed spaces defined by a Museliak-Orlicz function

In this paper, we introduce some new sequence spaces in n-normed spaces defined by Museliak-Orlicz function. Also we investigate some topological properties and inclusion relations between these Spaces

Representation of uniform boundedness principle and Hahn–Banach theorem in linear n-normed space

The concept of b-linear functional and its different types of continuity in linear n-normed space are presented and some of their properties are being established. We derive the Uniform Boundedness Principle and Hahn-Banach extension Theorem with the help of bounded b-linear functionals in the case of linear n-normed spaces and discuss some examples and applications. Finally, we present the concept of weak*convergence for the sequence of bounded b-linear functionals in linear n-normed space.

A-contraction mappings of integral type in n-normed spaces

In this article, A-contraction type mappings in integral case are defined on a complete n-normed spaces and the existence of some fixed point theorems are proved in the complete n-normed spaces and given some results on Picard operator.

On Hyperstability of the Cauchy Functional Equation in n-Banach Spaces

We present some hyperstability results for the well-known additive Cauchy functional equation f(x+y)=f(x)+f(y) in n-normed spaces, which correspond to several analogous outcomes proved for some other spaces. The main tool is a recent fixed-point theorem.

A-statistically localized sequences in n-normed spaces

In 1974, Krivonosov defined the concept of localized sequence that is defined as a generalization of Cauchy sequence in metric spaces. In this present work, the A-statistically localized sequences in n-normed spaces are defined and some main properties of A-statistically localized sequences are given. Also, it is shown that a sequence is A-statistically Cauchy iff its A-statistical barrier is equal to zero. Moreover, we define the uniformly A-statistically localized sequences on n-normed spaces and investigate its relationship with A-statistically Cauchy sequences.

Orlicz lacunary sequence spaces of 𝑙-fractional difference operators

Abstract Recently, S. K. Mahato and P. D. Srivastava [A class of sequence spaces defined by 𝑙-fractional difference operator, preprint 2018, http://arxiv.org/abs/1806.10383] studied 𝑙-fractional difference sequence spaces. In this article, we intend to make a new approach to introduce and study some lambda 𝑙-fractional convergent, lambda 𝑙-fractional null and lambda 𝑙-fractional bounded sequences over 𝑛-normed spaces. Various algebraic and topological properties of these newly formed sequence spaces have been explored, and some inclusion relations concerning these spaces are also established. Finally, some characterizations of the newly formed sequence spaces are given.

A Revisit to n-Normed Spaces Through Its Quotient Spaces

In this paper, we define several types of continuous mapping in $n$-normed spaces with respect to the norms of its quotient spaces. Then, we show that all types of the continuity are equivalent. We also study contractive mappings on $n$-normed spaces using these norms. In particular, we prove a fixed point theorem for contractive mappings on a closed and bounded set in the $n$-normed space with respect to the norms of its quotient spaces.In the last section we prove a fixed point theorem and give some remarks on the $p$-summable sequence space as an $n$-normed space.

Some new results on convergence, stability and data dependence in n-normed spaces

We introduce a new contractive condition and a new iterative method in n0normed space setting. We employ both of these to study convergence, stability, and data dependence. The results presented here extend and improve some recent results announced in the existing literature.

Bounded Linear Functional on n-Normed Spaces through Its Quotient Spaces

Bounded Linear Functional on n-Normed Spaces through Its Quotient Spaces

On the Aleksandrov problem for mappings preserving fuzzy n-distance in fuzzy n-normed spaces

On the Aleksandrov problem for mappings preserving fuzzy n-distance in fuzzy n-normed spaces

On Generalized Difference Ideal Convergence in Generalized Probabilistic n-normed Spaces

In this article, we introduce the concept of $$\varDelta ^{m}-I$$ -convergent and $$\varDelta ^{m}-I$$ Cauchy sequences in generalized probabilistic n-normed spaces and establish some results relating to this concept. We also study $$\varDelta ^{m}-I^{*}$$ convergence in the same space. Statement Probabilistic norm generalizes and unifies different notions of norm, represented by a distance function, rather than a positive real number. Ideal convergence unifies many notions of convergence of sequences. In this article, we have introduced the notion of generalized difference ideal convergent sequences in probabilistic n-normed space, which generalizes and unifies many existing notions. Hence, the results of this article have been established in general setting.