Search arXivSearch

arXiv · 2310.12161

Fixed Point Theorems Using Interpolative Boyd-Wong Type Contractions And Interpolative Matkowski Type Contractions on Partial Sb-Metric Space

Abstract

In this article, we define and explore the topological properties of partial Sb-metric space. We define interpolative Boyd-Wong type contraction and interpolative Matkowski type contractions in the setting of partial Sb-metric space and obtain fixed point results for the same.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Anuradha Gupta, Rahul Mansotra. 2023-09-27. Fixed Point Theorems Using Interpolative Boyd-Wong Type Contractions And Interpolative Matkowski Type Contractions on Partial Sb-Metric Space. https://arxiv.org/abs/2310.12161

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Exponentiable Objects and Function spaces in Lowen Fuzzy Topological Spaces

We study exponentiable objects and function spaces in the category of stratified Lowen fuzzy topological spaces over \(\I=[0,1]\). Using the Lowen fuzzy Sierpiński object \(\Sier\), which identifies \(τ_X\) with \(C(X,\Sier)\), we explicitly determine the largest splitting topology on this mapping set. Its open weights \(Φ:τ_X\to\I\) are precisely those satisfying Scott continuity and a finite-tier compatibility condition induced by finite powers of \(\Sier\). This yields an intrinsic characterization: \(X\) is exponentiable if and only if every \(μ\inτ_X\) satisfies \[ μ=\bigvee_{λ\triangleleftΦ} (\const{Φ(μ)}\wedgeλ), \qquad λ\triangleleftΦ \Longleftrightarrow \const{Φ(ν)}\wedgeλ\leqν \quad(ν\inτ_X). \] When this condition holds, \(Y^X\) has underlying set \(C(X,Y)\), with topology generated by \([Φ,v](f)=Φ(v\circ f)\). We also obtain a dual closed-set formulation and three applications. Exponentiability implies that \(τ_X\) is a continuous lattice, although the converse fails. Moreover, a classical space \(X\) is exponentiable exactly when its induced fuzzy space \(ωX\) is exponentiable in the entire stratified Lowen category. Finally, Lowen compact, strongly fuzzy compact, and \(N\)-compact Hausdorff spaces are exponentiable.

math.GN

Calibers of canonical hyperconnected spaces and their Vietoris hyperspaces

For infinite cardinals $λ\leq κ$, we calculate the calibers of topological spaces $X$ of cardinality $κ$ whose open sets are the subsets $A$ satisfying $|X \setminus A| < λ$. We also prove that the set of calibers of $X$ coincides with the set of calibers of the Vietoris hyperspace $\mathcal{H}(X)$, where the space $\mathcal{H}(X)$ has as its underlying set a collection of subsets of $X$ that includes all its finite subsets and is contained within the collection of its closed subsets.

math.GN

The circle as a topological fractal

We prove that no family of two continuous self-maps witnesses that the circle is a topological fractal, answering a question of Karasová and the present author. Since three maps are known to suffice, this bound is optimal. In contrast, for every $\varepsilon>0$ there are two continuous self-maps of the circle, depending on $\varepsilon$, whose images cover the circle and an integer $N$ such that every composition of $N$ of them has image of diameter less than $\varepsilon$. Thus two maps suffice at any prescribed scale, but no fixed pair works at all scales.

math.GN