Normed Spaces Research Articles

On ρ-statistical convergence in neutrosophic normed spaces

Abstract In this study, the concept of ρ-statistical convergence with respect to the neutrosophic norm in the neutrosophic normed spaces is introduced. Some properties and some inclusion theorems related to this concept are investigated.

Between norms and margins: The “Norms–Fringe–Margins” model. A dynamic model of psychosocial self-construction through an expanded notion of working

This article addresses the new forms and relationships to work currently developing, in line with the upheavals of the Anthropocene. Occupational and counseling psychology are developing models that increasingly integrate systemic and contextual dimensions to understand careers and work-related issues. We propose a theoretical model “Norms–Fringe–Margins” to approach these new forms of work as hybrid constructs, sources of both personal and social innovation. We argue that these new ways of relating to work can contribute to sustainable and just commitments to citizenship, both at the individual and social levels. The model distinguishes three interrelated spaces of psychosocial self-construction through work: a normed space (Norm), a space on the margin (Margin), and an intermediate space (Fringe). To analyze the psychosocial construction of a person, we study the dynamic interactions of these three psychosocial spaces as a presence supported by a set of tensions to overcome.

Sliding window method for measurable functions on neutrosophic normed spaces

We aim to introduce the nonnegative real-valued functions class and the research of Mursaleen and Mohiuddin. We introduce the sliding window idea approaches within the neutrosophic normed spaces range [0;∞) for real-valued measurable functions in order to accomplish aim. Additionally,using summability techniques, we derive a number of theorems and samples.

Criteria for the boundedness of a certain class of matrix operators from lpv into lqu

One of the main aims in the theory of matrices is to find necessary and sufficient conditions for the elements of any matrix so that the corresponding matrix operator maps continuously from one normed space into another one. Thus, it is very important to find the norm of the matrix operator, at least, to find upper and lower estimates of it. This problem in Lebesgue spaces of sequences in the general case is still open. This paper deals with the problem of boundedness of matrix operators from lpv into lqu for 1 < q < p < ∞, and we obtain necessary and sufficient conditions of this problem when matrix operators belong to the classes O2+- satisfying weaker conditions than Oinarov’s condition.

Remarks on Approximate Solutions to Difference Equations in Various Spaces

Quite often (e.g., using numerical methods), we are only able to find approximate solutions of some equations, and it is necessary to know the size of the difference between such approximate solutions and the mappings that satisfy the equation exactly. This issue is the main subject of the theory of Ulam stability, and it is related to other areas of research such as, e.g., shadowing, optimization, and approximation theory. In this expository paper, we present several selected outcomes on Ulam stability of difference equations, show possible extensions of them and indicate further directions for research. We also present and discuss some simple methods that allow improvement of several already known results concerning Ulam stability of some difference equations in normed or metric spaces and extend them to b-metric and 2-normed spaces. Our results show that the noticeable symmetry exists between the outcomes of this type in normed and metric spaces and those obtained by us for other spaces. In particular, we extend the result of Pólya and Szegö concerning the stability of equation xn+m=xn+xm for m,n∈T, where T means either the set of integers Z or the set of positive integers N. We also consider the stability of equation xn+p+a1xn+p−1+…+apxn+bn=0 (with a fixed positive integer p) and of two more general difference equations.

Convergence of the Cimmino algorithm for common fixed point problems with a countable family of operators

In this paper we apply Cimmino algorithm for common fixed point problems with a countable family of quasi-nonexpansive operators in an arbitrary normed space and show its convergence. Our results are an extension of the recent results by T. Y. Kong , H. Pajoohesh and G. T. Herman obtained for operators which are projections on convex closed sets in a finite-dimensional Euclidean space.

On α ̌–φ ̆-Fuzzy Contractive Mapping in Fuzzy Normed Space

تمثل فكرة النقاط الصامدة إحدى أقوى الأدوات الرياضية. الغرض الرئيسي من هذه الورقة هو تقديم نوع جديد من دالة الانكماش الضبابي في فضاء معياري ضبابي وهي "الدالة الانكماشية الضبابية ". نثبت بعض نتائج النقطه الصامدة لهذه الداله في سياق الفضاء المعياري الضبابي باستخدام الخاصية المثلثية للمعيار الضبابي. بالإضافة إلى ذلك ، في ظل ظروف محددة ، تم إثبات بعض النتائج الأخرى لهذا النوع من الدالة. أخيرًا ، يتم تقديم مثال لإظهار فائدة النتائج.

Componentwise Dinkelbach algorithm for nonlinear fractional optimization problems

The paper deals with fractional optimization problems where the objective function (ratio of two functions) is defined on a Cartesian product of two real normed spaces X and Y. Within this framework, we are interested to determine the so-called partial minimizers, i.e. points in X × Y with the property that any of its variables minimizes the objective function, restricted to this variable, with respect to the other one. While any global minimizer is obviously a partial minimizer, the reverse implication holds true only under additional assumptions (e.g. separability properties of the involved functions). By exploiting the particularities of the objective function, we deliver a Dinkelbach type algorithm for computing partial minimizers of fractional optimization problems. Further assumptions on the involved spaces and functions, such as Lipschitz-type continuity, partial Fréchet differentiability, and coercivity, enable us to establish the convergence of our algorithm to a partial minimizer.

A New Approach for the Statistical Convergence over Non-Archimedean Fields in Neutrosophic Normed Spaces

The goal of the research involves elaborating on the topics of statistical convergence, including statistical Cauchy sequences within non-Archimedean Neutrosophic normed spaces, as well as achieving specific useful conclusions. The present research shows how, within a non-Archimedean field, certain sections of statistically convergent sequences that could not be true often become true. Likewise, we created statistically complete and statistically continuous spaces for such regions that demonstrated certain essential facts. κ indicates a complete field of non-Archimedean and non-trivially valued research.

On Boltyanski and Gohberg's partition conjecture

AbstractIn 1965, Boltyanski and Gohberg made the following conjecture: Every bounded set in an ‐dimensional normed space can be divided into subsets of smaller diameters. In this paper, we prove the following result: Every bounded set in an ‐dimensional normed space can be divided into subsets of smaller diameters.

Convergence of the Jordan Neutrosophic Ideal in Neutrosophic Normed Spaces

Convergence of the Jordan Neutrosophic Ideal in Neutrosophic Normed Spaces

On best proximity point theorems for relatively nonexpansive mappings in locally convex spaces

Abstract This paper explores the concept of normal structure by introducing a generalized form known as P-proximal normal structure. Focusing on the framework of Hausdorff locally convex spaces, the study establishes optimal proximity outcomes for both cyclic and noncyclic relatively P-nonexpansive mappings. Furthermore, the paper presents in the realm of probabilistic normed spaces, considered as instances of Hausdorff locally convex spaces, some theorems that address the existence of best proximity points within this context.

On Ulam Stability with Respect to 2-Norm

The Ulam stability of various equations (e.g., differential, difference, integral, and functional) concerns the following issue: how much does an approximate solution of an equation differ from its exact solutions? This paper presents methods that allow to easily obtain numerous general Ulam stability results with respect to the 2-norms. In four examples, we show how to deduce them from the already known outcomes obtained for classical normed spaces. We also provide some simple consequences of our results. Thus, we demonstrate that there is a significant symmetry between such results in classical normed spaces and in 2-normed spaces.

Qproximinal and Qremotal in normed spaces

Qproximinal and Qremotal in normed spaces

Zabreiko’s lemma in 2-normed space and its applications

Zabreiko’s lemma in 2-normed space and its applications

Soft quasilinear operators in soft normed quasilinear spaces

In this study, we define soft quasilinear functionals on soft normed quasilinear spaces and we examine some of its qualities. By using the soft quasilinear operator defined in [6] we specify and prove some theorem related to the continuity and boundedness of soft quasilinear operators and functionals. Furthermore, we give some examples in favor of the soft quasilinear functionals.

On Non-linear Mappings Preserving the Semi-inner Product

We say that a smooth normed space X has a property (SL), if every mapping f:X rightarrow X preserving the semi-inner product on X is linear. It is well known that every Hilbert space has the property (SL) and the same is true for every finite-dimensional smooth normed space. In this paper, we establish several new results concerning the property (SL). We give a simple example of a smooth and strictly convex Banach space which is isomorphic to the space ell _p, but without the property (SL). Moreover, we provide a characterization of the property (SL) in the class of reflexive smooth Banach spaces in terms of subspaces of quotient spaces. As a consequence, we prove that the space ell _p have the property (SL) for every 1< p < infty . Finally, using a variant of the Gowers–Maurey space, we construct an infinite-dimensional uniformly smooth Banach space X such that every smooth Banach space isomorphic to X has the property (SL).

On rough deferred statistical convergence of difference sequences in [formula omitted]-fuzzy normed spaces

The current article broadly environs the introduction of rough deferred statistical convergence via difference operators as an extension of rough convergence, in the setting of L-fuzzy normed space. The paper also discusses the inevitable limit set of the novel convergence along with the proof of it being convex and closed with regard to the L-fuzzy norm. There is a further establishment of Δrj-deferred statistical cluster point and investigation of relations between the set of cluster points and the aforementioned convergence limit set.

Invertibility and Spectrum of the Riemann Boundary Value Problem Operator in a Countably Normed Space of Smooth Functions on a Circle

Invertibility and Spectrum of the Riemann Boundary Value Problem Operator in a Countably Normed Space of Smooth Functions on a Circle

Generalized Double Statistical Convergence Sequences on Ideals in Neutrosophic Normed Spaces

In this present research, having view in the Neutrosophic norm (u, v, w), which we presented I2-lacunary statistical convergence and I2-lacunary convergence strongly, looked into interactions between them, and made a few findings regarding the respective categories. At least went further to look at how both of such case approaches relate to I2-statistical convergence within the relevant Neutrosophic normed space.