Statistical Soft Wijsman Convergence

Erdal Bayram

Article Details

Statistical Soft Wijsman Convergence

Authors:

Erdal Bayram

Publisher:

Sakarya University

Main Topics:

Pure Mathematics (Other)

Journal:

Sakarya University Journal of Science Vol.28 Issue 6, pp.1342-1351

Document Type:

Article

Publication Date:

12/2024

Document Language:

English

Document ID (Org No.):

2001331525

pISSN:

2147-835X

Keywords:

Abstract:

 The concept of convergence is a fundamental tool for building or understanding a mathematical structure. In particular, many applied areas of mathematics require the analysis of sets or set-based approximations. A notable example is Wijsman convergence, a type of set convergence defined as the distance from a point to a set as determined by a metric function. Another important concept in our study is soft set theory, which generalizes classical set theory and provides an effective approach to addressing uncertainties in a parametric manner. Building on this foundation, we introduce the concepts of statistical and lacunary statistical convergence in the sense of Wijsman for sequences of closed sets within the framework of soft metric spaces. We establish fundamental properties associated with these types of convergence and explore their interrelationships, resulting in several inclusion results. Furthermore, we utilize a generalized version of the natural density function, referred to as the ϕ-weighted density function, to strengthen our findings.

 The concept of convergence is a fundamental tool for building or understanding a mathematical structure. In particular, many applied areas of mathematics require the analysis of sets or set-based approximations. A notable example is Wijsman convergence, a type of set convergence defined as the distance from a point to a set as determined by a metric function. Another important concept in our study is soft set theory, which generalizes classical set theory and provides an effective approach to addressing uncertainties in a parametric manner. Building on this foundation, we introduce the concepts of statistical and lacunary statistical convergence in the sense of Wijsman for sequences of closed sets within the framework of soft metric spaces. We establish fundamental properties associated with these types of convergence and explore their interrelationships, resulting in several inclusion results. Furthermore, we utilize a generalized version of the natural density function, referred to as the ϕ-weighted density function, to strengthen our findings.

 The concept of convergence is a fundamental tool for building or understanding a mathematical structure. In particular, many applied areas of mathematics require the analysis of sets or set-based approximations. A notable example is Wijsman convergence, a type of set convergence defined as the distance from a point to a set as determined by a metric function. Another important concept in our study is soft set theory, which generalizes classical set theory and provides an effective approach to addressing uncertainties in a parametric manner. Building on this foundation, we introduce the concepts of statistical and lacunary statistical convergence in the sense of Wijsman for sequences of closed sets within the framework of soft metric spaces. We establish fundamental properties associated with these types of convergence and explore their interrelationships, resulting in several inclusion results. Furthermore, we utilize a generalized version of the natural density function, referred to as the ϕ-weighted density function, to strengthen our findings.

 The concept of convergence is a fundamental tool for building or understanding a mathematical structure. In particular, many applied areas of mathematics require the analysis of sets or set-based approximations. A notable example is Wijsman convergence, a type of set convergence defined as the distance from a point to a set as determined by a metric function. Another important concept in our study is soft set theory, which generalizes classical set theory and provides an effective approach to addressing uncertainties in a parametric manner. Building on this foundation, we introduce the concepts of statistical and lacunary statistical convergence in the sense of Wijsman for sequences of closed sets within the framework of soft metric spaces. We establish fundamental properties associated with these types of convergence and explore their interrelationships, resulting in several inclusion results. Furthermore, we utilize a generalized version of the natural density function, referred to as the ϕ-weighted density function, to strengthen our findings.

Article Details

Statistical Soft Wijsman Convergence

Authors:

Erdal Bayram

Publisher:

Sakarya University

Main Topics:

Pure Mathematics (Other)

Journal:

Sakarya University Journal of Science Vol.28 Issue 6, pp.1342-1351

Document Type:

Article

Publication Date:

12/2024

Document Language:

English

Document ID (Org No.):

2001331525

pISSN:

2147-835X

Soft set

Soft metric

Wijsman convergence

Statistical convergence

Issues

Article Details

Statistical Soft Wijsman Convergence

Authors: Erdal Bayram

Publisher: Sakarya University

Main Topics: Pure Mathematics (Other)

Journal: Sakarya University Journal of Science Vol.28 Issue 6, pp.1342-1351

Document Type: Article

Publication Date: 12/2024

Document Language: English

Document ID (Org No.): 2001331525

pISSN: 2147-835X

Soft set

Soft metric

Wijsman convergence

Statistical convergence

Issues

Authors:

Erdal Bayram

Publisher:

Sakarya University

Main Topics:

Pure Mathematics (Other)

Journal:

Sakarya University Journal of Science Vol.28 Issue 6, pp.1342-1351

Document Type:

Article

Publication Date:

12/2024

Document Language:

English

Document ID (Org No.):

2001331525

pISSN:

2147-835X