Korean J. Math.  Vol 28, No 1 (2020)  pp.17-30
DOI: https://doi.org/10.11568/kjm.2020.28.1.17

$C^*$-algebra valued symmetric spaces and fixed point results with an application

Mohammad Asim, Mohammad Imdad


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.


C∗-algebra; C∗-algebra valued symmetric space, fixed point

Subject classification

47H10, 54H25


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A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl. 2012 (2012), Article ID 204. (Google Scholar)

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. (Google Scholar)

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. (Google Scholar)

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. (Google Scholar)

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. (Google Scholar)

S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fund. Math. 3 (1922), 133–181. (Google Scholar)

A. Branciari. A fixed point theorem of Banach–Caccioppoli type on a class of generalized metric spaces, Publ. Math. 57 (2000), 31–37. (Google Scholar)

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. (Google Scholar)

L. B. Ciric, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267–273. (Google Scholar)

S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1 (1) (1993), 5–11. (Google Scholar)

M. Imdad, M. Asim and R. Gubran, Common fixed point theorems for g- Generalized contractive mappings in b-metric spaces, Indian Journal of Mathematics 60 (1) (2018), 85–105. (Google Scholar)

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. (Google Scholar)

H. Long-Guang and Z. Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), 1468–1476. (Google Scholar)

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. (Google Scholar)

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. (Google Scholar)

S. G. Matthews, Partial metric topology, Annals of the New York Academy of Sciences 728 (1994), 183–197. (Google Scholar)

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). (Google Scholar)

J. Villa-Morales, Subordinate Semimetric Spaces and Fixed Point Theorems, J. Math. 2018 (2018), Article ID 7856594. (Google Scholar)

W. A. Wilson, On semi-metric spaces, American Journal of Mathematics 53 (2) (1931), 361–373. (Google Scholar)


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