C*-algebra valued quasi metric spaces and fixed point results with an application

Authors

DOI:

https://doi.org/10.4995/agt.2022.16783

Keywords:

C*-algebra, C-algebra valued quasi metric spaces, fixed point, integral equations

Abstract

In this paper, we introduce the notion of C*-algebra valued quasi metric space to generalize the notion of C*-algebra valued metric space and investigate the topological properties besides proving some core fixed point results. Finally, we employ our one of the main results to examine the existence and uniqueness of the solution for a system of Fredholm integral equations.

Downloads

Download data is not yet available.

Author Biographies

Mohammad Asim, Shree Guru Gobind Singh Tricentenary University

Assistant Professor, Department of Mathematics, Faculty of Science

Santosh Kumar, University of Dar es Salaam

Department of Mathematics, College of Natural and Applied Sciences

Associate Professor

(Fixed Point Theory)

Mohammad Imdad, Aligarh Muslim University

Professor, Department of Mathematics

Reny George, Prince Sattam bin Abdulaziz University

Professor, Department of Mathematics, College of Science and Humanities in Al-Kharj

References

A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl. 2012, Article ID 204. https://doi.org/10.1186/1687-1812-2012-204

M. Asim and M. Imdad, C*-algebra valued extended b-metric spaces and fixed point results with an application, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 82, no. 1 (2020), 207-218.

M. Asim and M. Imdad, C*-algebra valued symmetric spaces and fixed point results with an application, Korean J. Math. 28, no. 1 (2020), 17-30.

M. Asim, M. Imdad and S. Radenovic, Fixed point results in extended rectangular b-metric spaces with an application, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 81, no. 2 (2019), 43-50.

M. Asim, A. R. Khan and M. Imdad, Rectangular $M_{b}$-metric spaces and fixed point results, Journal of Mathematical Analysis 10, no. 1 (2019), 10-18. https://doi.org/10.1186/s13660-019-2223-3

M. Asim, A. R. Khan and M. Imdad, Fixed point results in partial symmetric spaces with an application, Axioms 8, no. 1 (2019): 13. https://doi.org/10.3390/axioms8010013

I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal., Gos. Ped. Inst. Unianowsk 30 (1989), 26-37.

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

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

S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis 1, no. 1 (1993), 5-11.

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

Z. H. Ma, L. N. Jiang and H. K. Sun, C*-algebra valued metric spaces and related fixed point theorems, Fixed Point Theory Appl. 2014, Article ID 206.

Z. H. Ma and L. N. Jiang, C*-algebra valued b-metric spaces and related fixed point theorems, Fixed Point Theory Appl. 2015, Article ID 222. https://doi.org/10.1186/s13663-015-0471-6

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

S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterranean Journal of Mathematics 11, no. 2 (2014), 703-711. https://doi.org/10.1007/s00009-013-0327-4

W. A. Wilson, On quasi-metric spaces, American Journal of Mathematics 53, no. 3 (1931), 675-684. https://doi.org/10.2307/2371174

Downloads

Published

2022-10-03

How to Cite

[1]
M. Asim, S. Kumar, M. Imdad, and R. George, “C*-algebra valued quasi metric spaces and fixed point results with an application”, Appl. Gen. Topol., vol. 23, no. 2, pp. 287–301, Oct. 2022.

Issue

Section

Articles