A Note on a Special Metric Space with Triple Fixed Points

Öz

This work is focused on constructing a general concept of triple fixed point of a mapping in a C*-algebra valued metric space. We also include some significant consequences of the hypotheses of our work in this paper. In addition, we provide some numerical examples for readers to see the connections between our work and other fields such as the theory of Integral Equations, Systems of Algebraic and Differential Equations and Dynamic Systems.

Anahtar Kelimeler

• C*-Algebra
• Triple Fixed Point
• Contraction Mapping
• Complete Metric Space
• Fixed Point Theory
• Cauchy Sequence.

Üçlü Sabit Noktalı Özel Bir Metrik Uzay Üzerine Bir Not

Öz

Bu çalışma, bir C*-cebiri değerli metrik uzayda bir eşlemenin üçlü sabit noktasının genel bir kavramını oluşturmaya odaklanmıştır. Makaleye, çalışmamıza ait varsayımların bazı önemli sonuçları da dahil edilmiştir. Bunun yanı sıra, elde edilen sonuçlarımızın uygulanabilirliğini göstermek amacı ile birkaç sayısal örnek verilmiştir. Ayrıca Banach Büzülme Prensibinin integral denklemler teorisi, türevli fonksiyonlar teorisi, cebirsel veya diferansiyel denklemler sistemi, dinamik sistemler vb. gibi bazı alanlara yönelik uygulamaları, bu tür alanlardaki diğer çalışmalardan örneklerle verilmiştir.

Anahtar Kelimeler

• C*-Cebir
• Üçlü Sabit Nokta
• Büzülme Dönüşümü
• Tam Metrik Uzayı
• Sabit Nokta Teorisi
• Cauchy Dizisi.

Kaynakça

1. Agarwal, R.P., Meehan, M. and O’Regan, D. (2001). Fixed point Theory and Application. Cambridge University Press, Cambridge (pp.170).
2. Berinde, V., Borcut, M. (2011). Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal, 74, 15, 4889-4897.
3. Berinde, V., Borcut, M. (2012). Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces. Appl. Math. Comput. 218(10), 5929-5936.
4. Borcut, M. (2012). Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces. Appl.Math. Comput. 218(14),7339-7346.
5. Ciric, L. (1981). Fixed Point Mappings on Compact Metric Spaces Publications De L’institut Mathematique Nouvelle serie, 30 (44), pp. 29-31.
6. Cosentino, M., Salimi, P., and Vetro, P. (2014). Fixed point results on metric-type spaces, Acta Math. Sci., 34(4), 1237-1253.
7. Gholamian, N., Khanehgir, M., and Allahyari, R. (2017). Some Fixed Point Theorems for C*-Algebra-Valued b2-Metric Spaces, Journal of Mathematical Extension Vol. 11, No. 2, 53-69.
8. Gupta, A., and Manro, S. (2017). A New Type of Tripled Fixed Point Theorem in Partially Ordered Complete Metric Space, Advances in Analysis, Vol. 2 (2), 63-70.

9. Harandi, A. (2013). Coupled and tripled fixed point theory in partially ordered metric spaces with applications to initial value problem, Mathematical and Computer Modeling 57, 2343-2348.
10. Jha, K. (2002). Some Applications of Banach Contraction Principle, Nepal Journal of Science and Technology, Vol.4, 135-140.
11. Lin, H. (2001). An Introduction to the Classification of Amenable C*-Algebras, https://doi.org/10.1142/4751, (2001), pp.332.
12. López, S.R. (2017). Metric spaces and the Banach fixed point theorem, Lecture Note.
13. Ma , Z., Jiang,l., and Sun,H. ( 2014). C*-Algebra-valued-metric spaces and related fixed point theorems, Fixed Point Theory and Application. 206, 1-11.
14. Murphy, GJ. (1990). C*-Algebras and Operator Theory. Academic Press, London, (pp.286)
15. Özer, Ö. and Omran, S. (2016). Common Fixed Point Theorems in C*-Algebra Valued b-Metric Spaces AIP Conference Proceedings 1773, 050005.
16. Özer, Ö. and Omran, S. (2017). On the Generalized C*-Valued Metric Spaces Related With Banach Fixed Point Theory, International Journal of Advanced and Applied Sciences, Vol.4, Issue.2, (2017), 35-37.
17. Özer, Ö. and Omran, S. (2019). A Note on C*-Algebra Valued G-Metric Space Related with Fixed Point Theorems, Bulletin of the Karaganda University- Mathematics, Vol.3 (95), 44-50.
18. Srinuvasa, B., Kishore, G.N.V., and Ramprasad, D. (2019). Some Tripled Fixed Point Theorems in Bipolar Metric Spaces, International Journal of Management, Technology and Engineering, Volume IX, Issue I, 715-730.
19. Wang, S. and Guo, B. (2011). Distance in Cone Metric Spaces and common fixed point theorems, Appl. Math Lett., 24, 1735-1739.