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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
12 Citations
1,842 Views
13 Pages

9 January 2022

We study spectral properties of a wide class of differential operators with frozen arguments by putting them into a general framework of rank-one perturbation theory. In particular, we give a complete characterization of possible eigenvalues for thes...

  • Tutorial
  • Open Access
11 Citations
2,669 Views
18 Pages

7 January 2022

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations fr...

  • Article
  • Open Access
1,833 Views
8 Pages

5 January 2022

The asymptotic behavior of resolvents of a proper convex lower semicontinuous function is studied in the various settings of spaces. In this paper, we consider the asymptotic behavior of the resolvents of a sequence of functions defined in a complete...

  • Article
  • Open Access
1,791 Views
11 Pages

2 January 2022

Analysis of power converter performance has tended to be engineering-oriented, focusing mainly on voltage stability, output power and efficiency improvement. However, there has been little discussion about the weight relations between these factors....

  • Article
  • Open Access
6 Citations
2,092 Views
17 Pages

2 January 2022

The objective of the research article is two-fold. Firstly, we present a fixed point result in the context of triple controlled metric type spaces with a distinctive contractive condition involving the controlled functions. Secondly, we consider an i...

  • Article
  • Open Access
1 Citations
1,739 Views
8 Pages

31 December 2021

In this paper, we develop some Hermite–Hadamard–Fejér type inequalities for n-times differentiable functions whose absolute values of n-th derivatives are (α,m)-convex function. The results obtained in this paper are extensio...

  • Article
  • Open Access
39 Citations
5,363 Views
16 Pages

An Improved Evaluation Methodology for Mining Association Rules

  • Fuguang Bao,
  • Linghao Mao,
  • Yiling Zhu,
  • Cancan Xiao and
  • Chonghuan Xu

31 December 2021

At present, association rules have been widely used in prediction, personalized recommendation, risk analysis and other fields. However, it has been pointed out that the traditional framework to evaluate association rules, based on Support and Confid...

  • Article
  • Open Access
13 Citations
3,269 Views
30 Pages

30 December 2021

Meningiomas are the most prevalent benign intracranial life-threatening brain tumors, with a life expectancy of a few months in the later stages, so this type of tumor in the brain image should be recognized and detected efficiently. The source of me...

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