Hilbert Journal of Mathematical Analysis

A new type of convergence in partial metric spaces

2025-04-10T09:21:37+07:00

In this paper, we introduce the concept of deferred statistical convergence in partial metric spaces (pms), extending classical notions of statistical convergence and summability. We define deferred Cesaro summability and investigate its fundamental properties. Connections between statistical convergence and deferred Cesaro summability are explored, including inclusion relationships and strictness. Additionally, we establish conditions under which deferred summability implies statistical convergence and vice versa. Examples and theorems are provided to illustrate the applicability and relevance of these concepts in partial metric spaces.

Intermediate spaces on weak type discrete Morrey spaces

2025-03-04T08:39:15+07:00

In this article we discuss inclusion between a discrete Morrey space and a weak discrete Morrey space as well as inclusion between two weak discrete Morrey spaces. By the inclusion properties of weak discrete Morrey spaces, we have intermediate spaces for the trivial case. Using the inclusion relation of discrete Morrey spaces and weak discrete Morrey spaces, we obtain that for the nontrivial case there is no weak discrete Morrey space between Banach pairs of weak discrete Morrey spaces except for the two weak discrete Morrey spaces itself.

Simplified computation of useful functions in linear canonical transform

2025-06-29T21:42:06+07:00

The linear canonical transform is an extension of the usual Fourier transform because the Fourier transform is a special form of the linear canonical transform. It also is a valuable tool in signal analysis. Many essential properties of the Fourier transform can be transferred in the linear canonical Fourier domain with some changes. In this research paper, we first introduce the interesting connection between the linear canonical transform and Fourier transform. It is shown that the relation can be developed to efficiently evaluate Gaussian function in the linear canonical transform domain. Some examples of the Gaussian function in the linear canonical domain are also presented to illustrate the result.

Inclusion between Bourgain-Morrey spaces and their weak types

2025-03-04T08:43:38+07:00

This paper aims to explore the embedding relation between Bourgain-Morrey spaces and weak Bourgain-Morrey spaces. Bourgain-Morrey Spaces are important function spaces in harmonic analysis. In this article, we introduce weak Bourgain-Morrey spaces as certain generalization of weak Morrey spaces. We investigate the necessary and sufficient conditions for functions in weak Bourgain-Morrey spaces to also be elements in Bourgain-Morrey spaces, and vice versa. Our result are inclusion between weak Bourgain-Morrey spaces and inclusion of weak Bourgain- Morrey spaces into a certain Bourgain-Morrey spaces. These result generelize the inclusion result in Morrey spaces, weak Morrey spaces, and Bourgain- Morrey spaces.