Sequence of Soft Points in Soft Δ-Metric Spaces

Abstract

In this paper, we have constructed a sequence of soft points in one soft set with respect to a fixed soft point of another soft set. The convergence and boundedness of these sequences in soft Δ-metric spaces are defined and their properties are established. Further, the complete soft Δ-metric spaces are introduced by defining soft Δ-Cauchy sequences.

Recurrence Relation Under Efros Theorem

“…e , ) and R x λ , S z δ ∈ ∆B(P a e , ) whenever n ≥ m, which contradicts the soft ∆-Hausdorff property of soft ∆-metric spaces [5]. Therefore,…”

“…Patil et al [5] introduced a new type of soft metric on two soft sets, namely, soft ∆-metric and is defined as, a mapping ∆ : SP (U 1 , Θ)×SP (U 2 , Θ) → R(Θ) + , the set of all positive soft real numbers, is said to be a soft ∆-metric on soft sets (U 1 , Θ) and…”

“…Further, the notions of soft ∆-open balls, soft ∆-closed balls, soft ∆-open sets and soft ∆-closed sets are introduced with their properties in [5].…”

“…By Theorem 2.2, R x λ is a soft ∆-limit point of (B, Θ), which is a contradiction to (B, Θ) is soft ∆-closed. Converse follows from the Theorem 2.2 and from [5].…”

Some New Results For Soft b-Metric Space

“…A. Tantawy , R. M. Hassan, [3], submitted the article deals with soft metric space up on soft set, where define soft metric function on it, he was encourage the other's to study soft compactness, soft continuous,…, in soft metric space also can gave more future works. In addition, in 2017 B. R. Wadkar, R. Bhardwaj, V. N. Mishra, B. Singh, [7] discovered at first one the definition of soft 𝑏 − metric space with some fundamentals of this concepts, finally in 2021 P. G. Patil1 and Nagashree N. Bhat, [5] introduced the sequence of soft points in soft metric space and generalized in to soft ∆-metric spaces with several theorems' bout its. The main aim of this article, is to study deeply the soft 𝑏 − metric space and introduce soft 𝑏 − convergent sequence, soft 𝑏 − bounded sequence, and soft 𝑏 − Cauchy sequence, in order to define soft 𝑏 − complete metric space, with several theorems relating on these concepts as well as generalization the proofs for theorems of numerical sequence on this subject.…”