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Axioms, Volume 11, Issue 1

January 2022 - 34 articles

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Cover Story: We consider the Banach space consisting of real functions defined on a metric space which is locally compact and countable at infinity. Additionally, we assume that functions belonging to the space in question have increments tempered by a given modulus of continuity. The mentioned space is normed by a suitable norm connected with the given modulus of continuity. We investigate as an important particular case the Euclidean space Rk as the locally compact and countable at infinity metric space. Moreover, we also provide a few particular examples of spaces of such a type with moduli of continuity generated by the Lipschitz or Holder conditions. The main result of the paper presents a sufficient condition for relative compactness in the discussed Banach space consisting of real functions defined on the space Rk with increments tempered by an arbitrary modulus of continuity. View this paper.

Articles (34)

  • Article
  • Open Access
179 Citations
14,370 Views
13 Pages

Brain Tumor Classification Using Dense Efficient-Net

  • Dillip Ranjan Nayak,
  • Neelamadhab Padhy,
  • Pradeep Kumar Mallick,
  • Mikhail Zymbler and
  • Sachin Kumar

17 January 2022

Brain tumors are most common in children and the elderly. It is a serious form of cancer caused by uncontrollable brain cell growth inside the skull. Tumor cells are notoriously difficult to classify due to their heterogeneity. Convolutional neural n...

  • Article
  • Open Access
33 Citations
2,628 Views
8 Pages

17 January 2022

Let G be a graph with a minimum degree δ of at least two. The inclusion chromatic index of G, denoted by χ⊂′(G), is the minimum number of colors needed to properly color the edges of G so that the set of colors incident with any v...

  • Article
  • Open Access
3 Citations
2,594 Views
9 Pages

Vector-Valued Entire Functions of Several Variables: Some Local Properties

  • Andriy Ivanovych Bandura,
  • Tetyana Mykhailivna Salo and
  • Oleh Bohdanovych Skaskiv

15 January 2022

The present paper is devoted to the properties of entire vector-valued functions of bounded L-index in join variables, where L:Cn→R+n is a positive continuous function. For vector-valued functions from this class we prove some propositions descr...

  • Article
  • Open Access
6 Citations
2,785 Views
19 Pages

A Family of Generalized Legendre-Based Apostol-Type Polynomials

  • Talha Usman,
  • Nabiullah Khan,
  • Mohd Aman and
  • Junesang Choi

14 January 2022

Numerous polynomials, their extensions, and variations have been thoroughly explored, owing to their potential applications in a wide variety of research fields. The purpose of this work is to provide a unified family of Legendre-based generalized Ap...

  • Article
  • Open Access
4 Citations
3,305 Views
31 Pages

14 January 2022

We establish some properties of the bilateral Riemann–Liouville fractional derivative Ds. We set the notation, and study the associated Sobolev spaces of fractional order s, denoted by Ws,1(a,b), and the fractional bounded variation spaces of f...

  • Article
  • Open Access
6 Citations
3,633 Views
19 Pages

10 January 2022

A numerical scheme for nonlinear hyperbolic evolution equations is made based on the implicit Runge-Kutta method and the Fourier spectral method. The detailed discretization processes are discussed in the case of one-dimensional Klein-Gordon equation...

  • Article
  • Open Access
1 Citations
2,477 Views
11 Pages

9 January 2022

We introduce the real minimal surfaces family by using the Weierstrass data (ζ−m,ζm) for ζ∈C, m∈Z≥2, then compute the irreducible algebraic surfaces of the surfaces family in three-dimensional Euclidean space E3. In...

  • Article
  • Open Access
5 Citations
2,230 Views
16 Pages

9 January 2022

First, semigroup structure is constructed by providing binary operations for the crossing cubic set structure. The concept of commutative crossing cubic ideal is introduced by applying crossing cubic set structure to commutative ideal in BCK-algebra,...

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