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

ALTINTAŞ İ., TAŞKÖPRÜ K.

Turkish Journal of Mathematics, vol.44, no.6, pp.2199-2216, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-2004-63
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2199-2216
  • Keywords: Elementary soft topology, soft compactness, soft cone metric, soft cover, soft fixed point, soft net
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© 2020. The American Society of Hematology. All Rights Reserved.Abstract: 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.