SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2018 / Volume: 67 Issue: 2

MELTEM ERDEN EGE AND CIHANGIR ALACA

Meltem Erden Ege
Cihangir Alaca
Pages
—
Publication Date
2018-08-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we prove a common fixed point theorem in C*-algebra-valued S-metric spaces defining new notions such as L-condition and k-contraction.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we present the concept of a C*-algebra-valued Smetric space.
📊
Key Findings & Data:We prove Banach contraction principle in this space.
💡
Conclusion & Impact:Finally, we prove a common fixed point theorem in C*-algebra-valued S-metric spaces defining new notions such as L-condition and k-contraction.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:Fixed point · C*-algebra · S-metric

Abstract

In this study, we present the concept of a C*-algebra-valued Smetric space. We prove Banach contraction principle in this space. Finally, we prove a common fixed point theorem in C*-algebra-valued S-metric spaces defining new notions such as L-condition and k-contraction.

🔖

Cite This Article

Ege, M. E., Alaca, C. (2018). MELTEM ERDEN EGE AND CIHANGIR ALACA. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 67 Issue: 2. https://ajindex.com/articles/1470055

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (42)

  1. Afra, J.M., Fixed point type theorem in S-metric spaces, Midd le-East Journal of Scienti…c Research, 22(6), (2014) 864–869.
  2. Afra, J.M., Double contraction in S-metric spaces, International Journal of Mathematical Analysis, 9(3), (2015), 117–125.
  3. Alsulami, H.H., Agarwal, R.P., Karapinar E. and Khojasteh, F., A short note on C -valued contraction mappings, Journal of Inequalities and Applications, (2016), 50.
  4. Bai, C., Coupled …xed point theorems in C*-algebra-valued b-metric spaces with application, Fixed Point Theory and Applications, (2016); 70.
  5. Batul S. and Kamran, T., C*-valued contractive type mappings, Fixed Point Theory and Applications, (2015), 142.
  6. Chouhan, P., A common unique …xed point theorem for expansive type mappings in S-metric spaces, International Mathematical Forum, 8, (2013) 1287–1293.
  7. Dung, N.V., Hieu N.T. and Radejovic, S., Fixed point theorems for g-monotone maps on partially ordered S-metric spaces, Filomat, 28(9), (2014) 1885–1898.
  8. Ege M.E. and Alaca, C., Some properties of modular S-metric spaces and its …xed point results, Journal of Computational Analysis and Applications, 20(1), (2016) 24–33.
  9. Gupta, A., Cyclic contraction on S-metric space, International Journal of Analysis and Ap- plications, 3(2), (2013) 119–130.
  10. Gupta V. and Deep, R., Some coupled …xed point theorems in partially ordered S-metric spaces, Miskolc Mathematical Notes, 16(1), (2015) 181–194.
  11. Hieu, N.T., Ly N.T.T. and Dung, N.V., A generalization of Ciric quasi-contractions for maps on S-metric spaces, Thai Journal of Mathematics, 13(2), (2015) 369–380.
  12. Isik H. and Turkoglu, D., Coupled …xed point theorems for new contractive mixed monotone mappings and applications to integral equations, Filomat, 28(6), (2014) 1253–1264.
  13. Kadelburg Z. and Radenovic, S., Fixed point results in C -algebra-valued metric spaces are direct consequences of their standard metric counterparts, Fixed Point Theory and Applica- tions, (2016); 53.
  14. Kamran, T., Postolache, M., Ghiura, A., Batul S. and Ali, R., The Banach contraction principle in C*-algebra-valued b-metric spaces with application, Fixed Point Theory and Applications, (2016);10.
  15. Klineam C. and Kaskasem, P., Fixed point theorems for cyclic contractions in C*-algebra- valued b-metric spaces, Journal of Function Spaces, Article ID 7827040 (2016).
  16. Lakshmikantham V. and Ciric, L., Coupled …xed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis, 70, (2009) 4341–4349.
  17. Ma, Z., Jiang L. and Xin, Q., Fixed point theorems on operator-valued metric space, Trans. Beijing Inst. Techol., 34(10), (2014) 1078–1080.
  18. Ma, Z., Jiang L. and Sun, H., C*-algebra-valued metric spaces and related …xed point theo- rems, Fixed Point Theory and Applications (2014), 2014:206.
  19. Ma Z., and Jiang, L., C*-algebra-valued b-metric spaces and related …xed point theorems, Fixed Point Theory and Applications, (2015), 2015:222.
  20. Murphy, G.J., C*-Algebras and Operator Theory, Academic Press, London (1990).
  21. Ozer O. and Omran, S., Common …xed point in C*-algebra b-valued metric space, AIP Conference Proceedings, (2016), 1173, 050005.
  22. Qiaoling, X., Lining J. and Ma, Z., Common …xed point theorems in C*-algebra valued metric spaces, Journal of Nonlinear Science and Applications, 9, (2016) 4617–4627.
  23. Sedghi, S., Altun I. and Shobe, N., Coupled …xed point theorems for contractions in fuzzy metric spaces, Nonlinear Analysis: Theory, Methods and Applications, 72(3-4), (2010) 1298–
  24. Sedghi, S., Shobe N. and Aliouche, A., A generalization of …xed point theorem in S-metric spaces, Mat. Vesnik, 64, (2012), 258–266.
  25. Sedghi S. and Dung, N.V., Fixed point theorems on S-metric spaces, Mat. Vesnik, 66, (2014), –124.
  26. Sedghi, S., Altun, I., Shobe, N. and Salahshour, M.A., Some properties of S-metric spaces and …xed point results, Kyungpook Mathematical Journal, 54(1), (2014) 113–122.
  27. Shateri, T.L., C*-algebra-valued modular spaces and …xed point theorems, Journal of Fixed Point Theory and Applications, 19(2), (2017) 1551–1560.
  28. Shehwar Dur-E. and Kamran, T., C*-valued G-contractions and …xed points, Journal of Inequalities and Applications, (2015), 2015:304.
  29. Shehwar, Dur-E, Batul, S., Kamran T. and Ghiura, A., Caristi’s …xed point theorem on C*-algebra valued metric spaces, Journal of Nonlinear Science and Applications, 9, (2016) –588.
  30. Tianqing, C., Some coupled …xed point theorems in C*-algebra-valued metric spaces, (2016) arXiv:1601.07168v1.
  31. Turkoglu D. and Binbasioglu, D., Coupled coincidence point theorems for compatible map- pings in ordered uniform space, Miskolc Mathematical Notes, 16(1), (2015) 527–541.
  32. Zada A. and Saifullah, S., Fixed point theorem for integral type C*-valued contraction, Journal of Analysis and Number Theory, 4(2), (2016) 101–104.
  33. Zada, A., Saifullah S. and Ma, Z., Common …xed point theorems for G-contraction in C*- algebra-valued metric spaces, International Journal of Analysis and Applications, (2016) (1), 23–27.
  34. Current address: Meltem ERDEN EGE (Corresponding author): Manisa Celal Bayar Univer- sity, Institute of Natural and Applied Sciences, Department of Mathematics, Yunusemre 45140 Manisa, Turkey
  35. E-mail address: [email protected] ORCID Address: Current address: Cihangir ALACA: Manisa Celal Bayar University, Faculty of Science and Arts, Department of Mathematics, Yunusemre 45140 Manisa, Turkey
  36. E-mail address: [email protected] ORCID Address: http://orcid.org/0000-0001-7777-8839
  37. Bai, C., Coupled …xed point theorems in C*-algebra-valued b-metric spaces with application, Fixed Point Theory and Applications, (2016); 70.
  38. Kadelburg Z. and Radenovic, S., Fixed point results in C -algebra-valued metric spaces are direct consequences of their standard metric counterparts, Fixed Point Theory and Applica- tions, (2016); 53.
  39. Kamran, T., Postolache, M., Ghiura, A., Batul S. and Ali, R., The Banach contraction principle in C*-algebra-valued b-metric spaces with application, Fixed Point Theory and Applications, (2016);10.
  40. Current address: Meltem ERDEN EGE (Corresponding author): Manisa Celal Bayar Univer- sity, Institute of Natural and Applied Sciences, Department of Mathematics, Yunusemre 45140 Manisa, Turkey
  41. E-mail address: [email protected] ORCID Address: Current address: Cihangir ALACA: Manisa Celal Bayar University, Faculty of Science and Arts, Department of Mathematics, Yunusemre 45140 Manisa, Turkey
  42. E-mail address: [email protected] ORCID Address: http://orcid.org/0000-0001-7777-8839