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Sanjay Roy

Publications and source records attributed to Sanjay Roy.

10 recordsLinked to original sources
arXiv2025

Fixed Point Theorems for TSR-Contraction Mapping in Probabilistic Metric Spaces

The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle, namely, TSR-contraction principle in various types of probabilistic metric spaces. The proposed contraction mapping is different from our traditional definitions of contraction mapping.

math.FA↗
arXiv2023

Characterization of Various Types of Fuzzy Delta Compactness Using Fuzzy Upper Limit of Fuzzy Delta Closed Sets

In this paper, we introduce the concept of various types fuzzy delta $(\delta)$ compactness such as Quasi fuzzy delta compact, Quasi fuzzy countably delta compact, Weakly fuzzy delta compact, $a$-delta compact, Strong fuzzy delta compact, Ultra fuzzy delta compact and Fuzzy delta compact and characterize these types of fuzzy delta compactness using the notion of fuzzy upper limit of net of some types of delta $(\delta)$ closed sets.

math.GM↗
arXiv2023

A Few Properties of $\delta$-Continuity and $\delta$-Closure on Delta Weak Topological Spaces

The main aim of this paper is to define a weakest topology $\sigma$ on a linear topological space $(E, \tau)$ such that each $\delta$-continuous functional on $(E, \tau)$ is $\delta$-continuous functional on $(E, \sigma)$ and to find out the relation between the set of these $\delta$-continuous functionals on $(E, \tau)$ and the set of all $\delta$-continuous functionals on $(E, \sigma)$. Also we find out the closure of a subset $A$ of $E$ on that weakest topology by the $\delta$-closure of $A$ with respect to the given topology.

math.GN↗
arXiv2023

A study on delta compact spaces

The aim of this paper is to introduce the concept of Delta-Compact spaces along with some basic properties of it. Here, we try to establish the behavior of Delta-Compact spaces under the continuous mapping. Finally, we define another concept namely, Locally Delta-Compactness.

math.GN↗
arXiv2021

Uniform Boundedness Principle and Hahn-Banach Theorem for b-linear functional related to linear 2-normed space

In this paper, we will see that the Cartesian product of two 2-Banach spaces is also 2-Banach space and discuss some properties of closed linear operator in linear 2-normed space. We also describe the concept of different types of continuity of b-linear functional and derive the Uniform Boundedness Principle and Hahn-Banach extension theorem for b-linear functionals in the case of linear 2-normed spaces. We also introduce the notion of weak*convergence for the sequence of bounded b-linear functionals relative to linear 2-normed space.

math.FA↗
arXiv2011

A Note on Hypervector Spaces

The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.

math.GM↗
arXiv2011

Innerproduct Hyperspaces

The main purpose of this paper is to generalize and develop a few basic properties of the innerproduct space on a hypervector space. On this hypervector space we define the norm. Also we establish a important relation between normed hyperspaces and innerproduct hyperspaces.

math.GM↗
arXiv2010

Cone Normed Linear Spaces

In this paper, we introduce cone normed linear space, study the cone convergence with respect to cone norm. Finally, we prove the completeness of a finite dimensional cone normed linear space.

math.GM↗
arXiv2010

A Note on Intuitionistic Fuzzy Hypervector Spaces

The notion of Intuitionistic fuzzy hypervector space has been generalized and a few basic properties on this concept are studied. It has been shown that the intersection and union of an arbitrary family of Intuitionistic fuzzy hypervector spaces are also Intuitionistic fuzzy hypervector space. Lastly, the notion of a linear transformation on a hypervector space is introduced and established an important theorem relative to Intuitionistic fuzzy hypervector spaces.

math.GM↗