Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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C* -ALGEBRA VALUED SYMMETRIC SPACES AND FIXED POINT RESULTS WITH AN APPLICATION

  • Received : 2019.09.03
  • Accepted : 2020.01.28
  • Published : 2020.03.30
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Abstract

In this paper, we firstly introduce the class of C*-algebra valued symmetric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of a solution for a system of Fredholm integral equations.

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References

  1. A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl. 2012 (2012), Article ID 204.
  2. M. Asim, A. R. Khan and M. Imdad. Rectangular Mb-metric spaces and fixed point results, Journal of mathematical analysis 10 (1) (2019), 10-18.
  3. M. Asim and M. Imdad. C*-algebra valued extended b-metric spaces and fixed point results with an application, U.P.B. Sci. Bull., Series A, Accepted.
  4. M. Asim, M. Imdad and S. Radenovic. Fixed point results in extended rectangular b-metric spaces with an application, U.P.B. Sci. Bull., Series A 81 (2) (2019), 11-20.
  5. M. Asim, A. R. Khan and M. Imdad. Fixed point results in partial symmetric spaces with an application, Axioms, 8(13), (2019), doi:10.3390.
  6. S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fund. Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
  7. A. Branciari. A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. 57 (2000), 31-37.
  8. S. Chandok, D. Kumar and C. Park, C*-algebra valued partial metric spaces and fixed point theorems, Proc. Indian Acad. Sci. (Math. Sci.) 129 (37) (2019), doi.org/10.1007/s12044-019-0481-0.
  9. L. B. Ciric, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267-273. https://doi.org/10.1090/S0002-9939-1974-0356011-2
  10. S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1 (1) (1993), 5-11.
  11. M. Imdad, M. Asim and R. Gubran, Common fixed point theorems for gGeneralized contractive mappings in b-metric spaces, Indian Journal of Mathematic, 60 (1) (2018), 85-105.
  12. M. Jleli and B. Samet. A generalized metric space and related fixed point theorems, Fixed Point Theory and Applications 2015:61 (2015), DOI 10.1186/s13663-015-0312-7.
  13. H. Long-Guang and Z. Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087
  14. Z. H. Ma, L. N. Jiang, H. K. Sun, C*-algebra valued metric spaces and related fixed point theorems, Fixed Point Theory Appl. 2014 (2014), Article ID 206.
  15. Z. H. Ma and L. N. Jiang, C*-algebra valued b-metric spaces and related fixed point theorems, Fixed Point Theory Appl. 2015 (2015), Article ID 222.
  16. S. G. Matthews, Partial metric topology, Annals of the New York Academy of Sciences 728 (1994), 183-197. https://doi.org/10.1111/j.1749-6632.1994.tb44144.x
  17. Z. Mustafa, J. R. Roshan, V. Parvaneh, and Z. Kadelburg. Some common fixed point results in ordered partial b-metric spaces, Journal of Inequalities and Applications 2013 (1) (2013).
  18. J. Villa-Morales, Subordinate Semimetric Spaces and Fixed Point Theorems, J. Math. 2018 (2018), Article ID 7856594.
  19. W. A. Wilson, On semi-metric spaces, American Journal of Mathematics 53 (2) (1931), 361-373. https://doi.org/10.2307/2370790