A Study on Parametric S-metric Spaces

Abstract

In this paper, some topological properties are discussed and some results on completeness, totally boundedness, compactness on parametric S-metric spaces are developed.

Some fixed point theorems in generalized parametric metric spaces and applications to ordinary differential equations

“…Proposition 1.5. [12] If P is a generalized parametric metric on X then P (a, b, •) is non-increasing function, ∀a, b ∈ X.…”

“…Definition 1.6. [12] Let (X, P, o) be a generalized parametric metric space. A sequence {x n } ⊆ X is said to be a (i) convergent sequence if there exists x ∈ X such that lim n→∞ P (x n , x, t) = 0, ∀t > 0.…”

“…Proposition 1.7. [12] Let (X, P, o) be a generalized parametric metric space and 'o' be continuous. Then (a) limit of a sequence is unique, if exist;…”

“…After that some researchers tried to generalize the concept of parametric metric in different approaches(viz. parametric-S metric [7,8], parametric A-metric [9], parametric N bmetric [10], parametric 2-metric [11] etc.). Analyzing such hybrid definitions of parametric metric, we introduced 'generalized parametric metric space' [12].…”

“…parametric-S metric [7,8], parametric A-metric [9], parametric N bmetric [10], parametric 2-metric [11] etc.). Analyzing such hybrid definitions of parametric metric, we introduced 'generalized parametric metric space' [12].…”