Topology of soft cone metric spaces

Altıntaş, İsmet; Şimşek, Dağıstan; Taşköprü, Kemal

doi:10.1063/1.5000605

Cited by 4 publications

(4 citation statements)

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“…by using the notion of soft element [18][19][20]. Also, works on fixed point theory have been ongoing over the soft sets, the soft metrics and soft cone metrics [21][22][23][24][25][26]. In recent years some authors studied on 𝜖-soft topological spaces by using elementary operations on soft sets [27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

On elementary soft compact topological spaces

Altıntaş¹

2021

MANAS Journal of Engineering

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Section: Introductionmentioning

confidence: 99%

On elementary soft compact topological spaces

Altıntaş¹

2021

MANAS Journal of Engineering

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“…Abbas et al [3] proved several important fixed point theorems in soft metric spaces via the soft point. Şimşek et al [41] introduced soft cone metric structure using the soft element notation that are different from the soft points and proved several fixed point theorems and Altıntaş et al [4] studied the elementary soft topology of soft cone metric spaces.…”

Section: Introductionmentioning

confidence: 99%

“…Altıntaş et al. [4] showed that all soft cone metric spaces are not an elementary soft topological spaces. However, with some restriction [see (D4)], a soft cone metric space becomes an elementary soft topological space.…”

Section: Introductionmentioning

confidence: 99%

Compactness of soft cone metric space and fixed point theorems related to diametrically contractive mapping

Altıntaş¹,

Taşköprü²

2020

Turk J Math

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In this article, we describe the concepts such as sequentially soft closeness, sequential compactness, totally boundedness and sequentially continuity in any soft cone metric space and prove their some properties. Also, we examine soft closed set, soft closure, compactness and continuity in an elementary soft topological cone metric space. Unlike classical cone metric space, sequential compactness and compactness are not the same here. Because the compactness is an elementary soft topological property and cannot be defined for every soft cone metric space. However, in the restricted soft cone metric spaces, they are the same. Additionally, we prove some fixed point theorems related to diametrically contractive mapping in a complete soft cone metric space.

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“…Immediately afterwards, in this paper we focus on Jungck's common fixed point consequences for commuting mappings [9] and present some theorems in rectangular soft metric spaces. More details on fixed point theorems and common fixed point theorems can be found at [1,3,6,7,10,[13][14][15][16]21].…”

Section: Introductionmentioning

confidence: 99%