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Year 2022, Issue: 41, 70 - 81, 31.12.2022

Hande Poşul Çiğdem Gündüz Servet Kütükcü

https://doi.org/10.53570/jnt.1177525
Cited By: 1

Abstract

References

  • M. Fréchet, Sur Quelques Points du Calcul Fonctionnel, Rendiconti del Circolo Mathematico di Palermo 22 (1906) 1–72.
  • S. Gahler, 2-Metrische Raume und Iher Topoloische Struktur, Mathematische Nachrichten 26 (1963) 115–148.
  • B. C. Dhage, Generalized Metric Spaces Mappings with Fixed Point, Bulletin of Calcutta Mathematical Society 84 (1992) 329–336.
  • Z. Mustafa, B. Sims, A New Approach to Generalized Metric Spaces, Journal of Nonlinear and Convex Analysis 7 (2) (2006) 289–297.
  • S. Sedghi, N. Shobe, H. Zhou, A Common Fixed Point Theorem in D_-Metric Spaces, Fixed Point Theory and Applications 2007 (2007) 1–13.
  • S. Sedghi, N. Shobe, A. Aliouche, A Generalization of Fixed Point Theorem in S-Metric Spaces, Matematicki Vesnik 64 (3) (2012) 258–266.
  • M. Abbas, B. Ali, Y. I. Suleiman, Generalized Coupled Common Fixed Point Results in Partially Ordered A-Metric Spaces, Fixed Point Theory and Applications 64 (2015) 1–24.
  • D. Molodtsov, Soft Set Theory-First Results, Computers & Mathematics with Applications 37 (4-5) (1999) 19–31.
  • P. K. Maji, R. Biswas, A. R. Roy, Soft Set Theory, Computers & Mathematics with Applications 45 (4-5) (2003) 555–562.
  • K. V. Babitha, J. J. Sunil, Soft Set Relations and Functions, Computers & Mathematics with Applications 60 (7) (2010) 1840–1849.
  • Ç. Gündüz Aras, H. Poşul, On Some New Operations in Probabilistic Soft Set Theory, European Journal of Pure and Applied Mathematics 9 (3) (2016) 333–339.
  • D. Pei, D. Miao, From Soft Sets to Information Systems, IEEE International Conference on Granular Computing 2 (2005) 617–621.
  • S. Bayramov, Ç. Gündüz Aras, A New Approach to Separability and Compactness in Soft Topological Spaces, TWMS Journal of Pure and Applied Mathematics 9 (1) (2018) 82–93.
  • S. Bayramov, Ç. Gündüz Aras, L. Mdzinarishvili, Singular Homology Theory in The Category of Soft Topological Spaces, Georgian Mathematical Journal 22 (4) (2015) 457–467.
  • M. Shabir, M. Naz, On Soft Topological Spaces, Computers & Mathematics with Applications 61 (7) (2011) 1786–1799.
  • N. Taş, N. Y. Özgür, P. Demir, An Application of Soft Set and Fuzzy Soft Set Theories to Stock Management, Süleyman Demirel University Journal of Natural and Applied Sciences 21 (3) (2017) 791–796.
  • T. M. Al-shami, L. D. R. Kocinac, The Equivalence Between The Enriched and Extended Soft Topologies, Applied and Computational Mathematics 18 (2) (2019) 149–162.
  • Ç. Gündüz Aras, S. Bayramov, On the Tietze Extension Theorem in Soft Topological Spaces, Proceedings of The Institute of Mathematics and Mechanics 43 (1) (2017) 105–115.
  • S. Bayramov, Ç. Gündüz, Soft Locally Compact Spaces and Soft Paracompact Spaces, Journal of Mathematics and System Science 3 (2013) 122–130.
  • S. Hussain, B. Ahmad, Some Properties of Soft Topological Spaces, Computers & Mathematics with Applications 62 (11) (2011) 4058–4067.
  • N. Çağman, S. Karataş, S. Enginoğlu, Soft Topology, Computers and Mathematics with Applications 62 (2011) 351–358.
  • T. Aydın, S. Enginoğlu, Some Results on Soft Topological Notions, Journal of New Results in Science 10 (1) (2021) 65–75.
  • S. Enginoğlu, N. Çağman, S. Karataş, T. Aydın On Soft Topology, El-Cezerî Journal of Science and Engineering 2 (3) (2015) 23–38.
  • N. Çağman, S. Enginoğlu, Soft Set Theory and Uni{Int Decision Making, European Journal of Operational Research 207 (2) (2010) 848–855.
  • S. Das, S. K. Samanta, Soft Metric, Annals of Fuzzy Mathematics and Informatics 6 (1) (2013) 77–94.
  • M. Riaz, Z. Fatima, Certain Properties of Soft Metric Spaces, Journal of Fuzzy Mathematics 25 (3) (2017) 543–560.
  • B. R. Wadkar, B. Singh, R. Bhardwaj, Coupled Fixed Point Theorems with Monotone Property in Soft b-Metric Space, International Journal of Mathematical Analysis 11 (8) (2017) 363–375.
  • S. Bayramov, Ç. Gündüz Aras, H. Poşul, Bipolar Soft Metric Spaces, Filomat (Accepted).
  • N. Bilgili Güngör, Fixed Point Results From Soft Metric Spaces and Soft Quasi Metric Spaces to Soft G-Metric Spaces, TWMS Journal of Applied and Engineering Mathematics 10 (1) (2020) 118–127.
  • A. C. Güler, E. D. Yıldırım, A Note on Soft G-Metric Spaces About Fixed Point Theorems, Annals of Fuzzy Mathematics and Informatics 12 (5) (2016) 691–701.
  • Ç. Gündüz Aras, S. Bayramov, M. İ. Yazar, Soft D-Metric Spaces, Boletim da Sociedade Paranaense de Matem_atica 38 (7) (2020) 137–147.
  • Ç. Gündüz Aras, S. Bayramov, Vefa Cafarli, A study on soft S-metric spaces, Communications in Mathematics and Applications 9 (4) (2018) 713–723.

Soft $A$-Metric Spaces

Year 2022, Issue: 41, 70 - 81, 31.12.2022

Hande Poşul Çiğdem Gündüz Servet Kütükcü

https://doi.org/10.53570/jnt.1177525
Cited By: 1

Abstract

This paper draws on the theory of soft $A$-metric space using soft points of soft sets and the concept of $A$-metric spaces. This new space has great importance as a new type of generalisation of metric spaces since it includes various known metric spaces. In this paper, we introduce the concept of soft $A$-metric space and examine the relations with known spaces. Then, we examine various basic properties of these spaces: soft Hausdorffness, a soft Cauchy sequence, and soft convergence.

Keywords

Soft metric A-metric soft A-metric

References

  • M. Fréchet, Sur Quelques Points du Calcul Fonctionnel, Rendiconti del Circolo Mathematico di Palermo 22 (1906) 1–72.
  • S. Gahler, 2-Metrische Raume und Iher Topoloische Struktur, Mathematische Nachrichten 26 (1963) 115–148.
  • B. C. Dhage, Generalized Metric Spaces Mappings with Fixed Point, Bulletin of Calcutta Mathematical Society 84 (1992) 329–336.
  • Z. Mustafa, B. Sims, A New Approach to Generalized Metric Spaces, Journal of Nonlinear and Convex Analysis 7 (2) (2006) 289–297.
  • S. Sedghi, N. Shobe, H. Zhou, A Common Fixed Point Theorem in D_-Metric Spaces, Fixed Point Theory and Applications 2007 (2007) 1–13.
  • S. Sedghi, N. Shobe, A. Aliouche, A Generalization of Fixed Point Theorem in S-Metric Spaces, Matematicki Vesnik 64 (3) (2012) 258–266.
  • M. Abbas, B. Ali, Y. I. Suleiman, Generalized Coupled Common Fixed Point Results in Partially Ordered A-Metric Spaces, Fixed Point Theory and Applications 64 (2015) 1–24.
  • D. Molodtsov, Soft Set Theory-First Results, Computers & Mathematics with Applications 37 (4-5) (1999) 19–31.
  • P. K. Maji, R. Biswas, A. R. Roy, Soft Set Theory, Computers & Mathematics with Applications 45 (4-5) (2003) 555–562.
  • K. V. Babitha, J. J. Sunil, Soft Set Relations and Functions, Computers & Mathematics with Applications 60 (7) (2010) 1840–1849.
  • Ç. Gündüz Aras, H. Poşul, On Some New Operations in Probabilistic Soft Set Theory, European Journal of Pure and Applied Mathematics 9 (3) (2016) 333–339.
  • D. Pei, D. Miao, From Soft Sets to Information Systems, IEEE International Conference on Granular Computing 2 (2005) 617–621.
  • S. Bayramov, Ç. Gündüz Aras, A New Approach to Separability and Compactness in Soft Topological Spaces, TWMS Journal of Pure and Applied Mathematics 9 (1) (2018) 82–93.
  • S. Bayramov, Ç. Gündüz Aras, L. Mdzinarishvili, Singular Homology Theory in The Category of Soft Topological Spaces, Georgian Mathematical Journal 22 (4) (2015) 457–467.
  • M. Shabir, M. Naz, On Soft Topological Spaces, Computers & Mathematics with Applications 61 (7) (2011) 1786–1799.
  • N. Taş, N. Y. Özgür, P. Demir, An Application of Soft Set and Fuzzy Soft Set Theories to Stock Management, Süleyman Demirel University Journal of Natural and Applied Sciences 21 (3) (2017) 791–796.
  • T. M. Al-shami, L. D. R. Kocinac, The Equivalence Between The Enriched and Extended Soft Topologies, Applied and Computational Mathematics 18 (2) (2019) 149–162.
  • Ç. Gündüz Aras, S. Bayramov, On the Tietze Extension Theorem in Soft Topological Spaces, Proceedings of The Institute of Mathematics and Mechanics 43 (1) (2017) 105–115.
  • S. Bayramov, Ç. Gündüz, Soft Locally Compact Spaces and Soft Paracompact Spaces, Journal of Mathematics and System Science 3 (2013) 122–130.
  • S. Hussain, B. Ahmad, Some Properties of Soft Topological Spaces, Computers & Mathematics with Applications 62 (11) (2011) 4058–4067.
  • N. Çağman, S. Karataş, S. Enginoğlu, Soft Topology, Computers and Mathematics with Applications 62 (2011) 351–358.
  • T. Aydın, S. Enginoğlu, Some Results on Soft Topological Notions, Journal of New Results in Science 10 (1) (2021) 65–75.
  • S. Enginoğlu, N. Çağman, S. Karataş, T. Aydın On Soft Topology, El-Cezerî Journal of Science and Engineering 2 (3) (2015) 23–38.
  • N. Çağman, S. Enginoğlu, Soft Set Theory and Uni{Int Decision Making, European Journal of Operational Research 207 (2) (2010) 848–855.
  • S. Das, S. K. Samanta, Soft Metric, Annals of Fuzzy Mathematics and Informatics 6 (1) (2013) 77–94.
  • M. Riaz, Z. Fatima, Certain Properties of Soft Metric Spaces, Journal of Fuzzy Mathematics 25 (3) (2017) 543–560.
  • B. R. Wadkar, B. Singh, R. Bhardwaj, Coupled Fixed Point Theorems with Monotone Property in Soft b-Metric Space, International Journal of Mathematical Analysis 11 (8) (2017) 363–375.
  • S. Bayramov, Ç. Gündüz Aras, H. Poşul, Bipolar Soft Metric Spaces, Filomat (Accepted).
  • N. Bilgili Güngör, Fixed Point Results From Soft Metric Spaces and Soft Quasi Metric Spaces to Soft G-Metric Spaces, TWMS Journal of Applied and Engineering Mathematics 10 (1) (2020) 118–127.
  • A. C. Güler, E. D. Yıldırım, A Note on Soft G-Metric Spaces About Fixed Point Theorems, Annals of Fuzzy Mathematics and Informatics 12 (5) (2016) 691–701.
  • Ç. Gündüz Aras, S. Bayramov, M. İ. Yazar, Soft D-Metric Spaces, Boletim da Sociedade Paranaense de Matem_atica 38 (7) (2020) 137–147.
  • Ç. Gündüz Aras, S. Bayramov, Vefa Cafarli, A study on soft S-metric spaces, Communications in Mathematics and Applications 9 (4) (2018) 713–723.
There are 32 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Hande Poşul 0000-0003-3027-8460

Çiğdem Gündüz 0000-0002-3033-9772

Servet Kütükcü 0000-0002-2513-1600

Publication Date December 31, 2022
Submission Date September 20, 2022
Published in Issue Year 2022 Issue: 41

Cite

APA Poşul, H., Gündüz, Ç., & Kütükcü, S. (2022). Soft $A$-Metric Spaces. Journal of New Theory(41), 70-81. https://doi.org/10.53570/jnt.1177525
AMA Poşul H, Gündüz Ç, Kütükcü S. Soft $A$-Metric Spaces. JNT. December 2022;(41):70-81. doi:10.53570/jnt.1177525
Chicago Poşul, Hande, Çiğdem Gündüz, and Servet Kütükcü. “Soft $A$-Metric Spaces”. Journal of New Theory, no. 41 (December 2022): 70-81. https://doi.org/10.53570/jnt.1177525.
EndNote Poşul H, Gündüz Ç, Kütükcü S (December 1, 2022) Soft $A$-Metric Spaces. Journal of New Theory 41 70–81.
IEEE H. Poşul, Ç. Gündüz, and S. Kütükcü, “Soft $A$-Metric Spaces”, JNT, no. 41, pp. 70–81, December 2022, doi: 10.53570/jnt.1177525.
ISNAD Poşul, Hande et al. “Soft $A$-Metric Spaces”. Journal of New Theory 41 (December 2022), 70-81. https://doi.org/10.53570/jnt.1177525.
JAMA Poşul H, Gündüz Ç, Kütükcü S. Soft $A$-Metric Spaces. JNT. 2022;:70–81.
MLA Poşul, Hande et al. “Soft $A$-Metric Spaces”. Journal of New Theory, no. 41, 2022, pp. 70-81, doi:10.53570/jnt.1177525.
Vancouver Poşul H, Gündüz Ç, Kütükcü S. Soft $A$-Metric Spaces. JNT. 2022(41):70-81.

Cited By

BIPOLAR SOFT CONTINUITY ON BIPOLAR SOFT TOPOLOGICAL SPACES
Maltepe Journal of Mathematics
https://doi.org/10.47087/mjm.1314428
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