Some soft topological properties and fixed soft element results in soft complex valued metric spaces

Some soft topological properties and fixed soft element results in soft complex valued metric spaces

In this paper, first, by using the idea of soft complex numbers as in Das and Samanta [8], we introduce thenotion of soft complex valued metric spaces and investigate some of their topological aspects. Next, we establish somefixed soft element theorems for various soft mappings on soft complex valued metric spaces, which are the main resultsof our paper.

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  • [1] Abbas M, Arshad M, Azam A. Fixed points of asymptotically regular mappings in complex-valued metric spaces. Georgian Mathematical Journal 2013; 20 (2): 213-221.
  • [2] Abbas M, Murtaza G, Romaguera S. On the fixed point theory of soft metric spaces. Fixed Point Theory and Applications 2016; 2016 (17). doi:10.1186/1687-1812-2012-88.
  • [3] Ali MI, Feng F, Liu X, Min WK, Shabir M. On some new operations in soft set theory. Computers and Mathematics with Applications 2009; 57: 1547-1553.
  • [4] Azam A, Fisher B, Khan M. Common fixed point theorems in complex valued metric spaces. Numerical Functional Analysis and Optimization 2011; 32 (3): 243-253.
  • [5] Das S, Majumdar P, Samanta SK. On soft linear spaces and soft normed linear spaces. Annals of Fuzzy Mathematics and Informatics 2015; 9 (1): 91-109.
  • [6] Das S, Samanta SK. Soft real sets, soft real numbers and their properties. Journal of Fuzzy Mathematics 2012; 20 (3): 551-576.
  • [7] Das S, Samanta SK. On soft metric spaces. Journal of Fuzzy Mathematics 2013; 21(3): 1-28.
  • [8] Das S, Samanta SK. On soft complex sets and soft complex numbers. Journal of Fuzzy Mathematics 2013; 21 (1): 195-216.
  • [9] Demir İ, Özbakır OB, Yıldız İ. On fixed soft element theorems in se-uniform spaces. Journal of Nonlinear Sciences and Applications 2016; 9: 1230-1242.
  • [10] Fernandez JR, Gallego I, Jimenez-Losada A, Ordonez M. Soft cooperation systems and games. International Journal of General Systems 2018; 47 (3): 244-262.
  • [11] Güler AÇ, Yıldırım ED, Özbakır OB. A fixed point theorem on soft G-metric spaces. Journal of Nonlinear Sciences and Applications 2016; 9: 885-894.
  • [12] Kandemir MB. The concept of σ -algebraic soft set. Soft Computing 2018; 22: 4353-4360.
  • [13] Maji PK, Biswas R, Roy AR. Soft set theory. Computers and Mathematics with Applications 2003; 45: 555-562.
  • [14] Molodtsov D. Soft set theory-first results. Computers and Mathematics with Applications 1999; 37: 19-31.
  • [15] Nashine HK, Imdad M, Hasan M. Common fixed point theorems under rational contractions in complex valued metric spaces. Journal of Nonlinear Sciences and Applications 2014; 7: 42-50.
  • [16] Nazmul S, Samanta SK. Neighbourhood properties of soft topological spaces. Annals of Fuzzy Mathematics and Informatics 2013; 6 (1): 1-15.
  • [17] Özbakır OB, Demir İ. On the soft uniformity and its some properties. Journal of Mathematics and Computer Science 2015; 5 (6): 762-779.
  • [18] Pei D, Miao D. From soft sets to information systems. in: X. Hu, Q. Liu, A. Skowron, T.Y. Lin, R.R. Yager, B. Zhang (Eds.), Proceedings of Granular Computing, IEEE 2005; 2: 617-621.
  • [19] Rouzkard F, Imdad M. Some common fixed point theorems on complex valued metric spaces. Computers and Mathematics with Applications 2012; 64(6): 1866-1874.
  • [20] Shabir M, Naz M. On soft topological spaces. Computers and Mathematics with Applications 2011; 61: 1786-1799.
  • [21] Sintunavarat W, Cho YJ, Kumam P. Urysohn integral equations approach by common fixed points in complexvalued metric spaces. Advances in Difference Equations 2013; 2013(49).
  • [22] Wardowski D. On a soft mapping and its fixed points. Fixed Point Theory and Applications 2013; 2013 (182).