C*-ALGEBRA-VALUED b-METRIC-LIKE SPACE AND SOME FIXED POINT THEOREMS
Keywords:
C∗-algebra, metric-like, b-metric, fixed point
Abstract
In this article, we initiate the notion of C∗-algebra valued b- metric-like space. The Banach and Kannan fixed point results are examined in such space. Contrasting examples are formulated to show that the proposed ideas herein are novel and extend some important significant results in the literature.
References
[1] Ahmad, Z. T., Shagari, M. S., Noorwali, M., Tijjani, A. A. and Saliu, A. (2025). An Introduction to C∗-algebra-valued metric-like space with related appplications. J. Maths. 2025, Article ID 4878114, https://doi.org/10.1155/jom/4878114.
[2] Ahmad, Z. T., Shagari, M. S., and Tijjani, A. A. (2025). Notes on fixed point results of C∗-algebra-valued metric space. MACA, e725608.
[3] Alghamdi, M. A., Hussain, N. and Salimi, P. (2013). Fixed point and coupled fixed point theorems on b-metric-like spaces. J. Inequal. and Appl. vol. 2013, article 402.
[4] Amini-Harandi, A. (2012). Metric-like spaces, partial metric space and fixed points. J. Fixed Point Theory Appl. 2012, 204
[5] Bakhtin, I. A. (1989). The contraction mapping principle in almost metric space. Funct. Anal. 30, 2637.
[6] Chandok, S., Kumar, D. and Park, C. (2019). C∗-algebra-valued partial metric space and fixed point theorems. Proc. Indian Acad. Sci. (Math. Sci.), 129(37).
[7] Czerwik, S. (1993). Contraction mappings in b-metric space. Acta Math. Inform. Univ. Ostrav. 30, 511.
[8] Douglas, R. G. (1998). Banach algebra techniques in operator theory. Spring. Berlin.
[9] Hitzler, P. and Seda, A. K. (2000). Dislocated topologies. J. Electron. Eng. 51(12), 37.
[10] Hosseini, A. and Fosner, A. (2019). The Structure of Metric-like Spaces. Sah. Comm. in Math. Analy. (SCMA). 14(1), 159-171.
[11] Hussain, N., Roshan, J. R., Parvaneh, V., and Kadelburg, Z. (2014). Fixed Points of Con- tractive Mappings in bMetricLike Spaces. The Scientific World Journal, 2014(1), 471827.
[12] Ma, Z., Jiang, L. and Sun, H. (2014). C∗-algebra-valued metric space and related fixed point theorems. J. Fixed Point Theory and Appl., 206:111.
[13] Ma, Z. and Jiang, L. (2015). C∗-algebra-valued b-metric space and related fixed point theorems. J. Fixed Point Theory and Appl., 2015(1), 222.
[14] Madadi, M., ORegan, D., Park, C., de la Sen, M. and Saadati, R. (2020). On the Topology Induced by C∗-algebra-valued fuzzy metric space. Mathematics, 8(6), 905.
[15] Maheswari, J. U., Anbarasan, A., Gunaseelan, M., Parvaneh, V. and Bonab, S. H.(2022). Solving an integral equation via C∗-algebra-valued partial b-metrics. J. Fixed Point Theory Algorithms Sci. Eng., 18.
[16] Matthews, S. G. (1994). Partial metric topology. In: Proc. 8th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci., vol. 728, pp. 183-197.
[17] Mlaiki, N., Asim, M., and Imdad, M. (2020). C∗-algebra-valued partial b-metric space and fixed point results with an application. Mathematics, 8(8), 1381.
[18] Murphy, G. J.(1990). C∗-Algebras and Operator Theory. Academic Press, London.
[2] Ahmad, Z. T., Shagari, M. S., and Tijjani, A. A. (2025). Notes on fixed point results of C∗-algebra-valued metric space. MACA, e725608.
[3] Alghamdi, M. A., Hussain, N. and Salimi, P. (2013). Fixed point and coupled fixed point theorems on b-metric-like spaces. J. Inequal. and Appl. vol. 2013, article 402.
[4] Amini-Harandi, A. (2012). Metric-like spaces, partial metric space and fixed points. J. Fixed Point Theory Appl. 2012, 204
[5] Bakhtin, I. A. (1989). The contraction mapping principle in almost metric space. Funct. Anal. 30, 2637.
[6] Chandok, S., Kumar, D. and Park, C. (2019). C∗-algebra-valued partial metric space and fixed point theorems. Proc. Indian Acad. Sci. (Math. Sci.), 129(37).
[7] Czerwik, S. (1993). Contraction mappings in b-metric space. Acta Math. Inform. Univ. Ostrav. 30, 511.
[8] Douglas, R. G. (1998). Banach algebra techniques in operator theory. Spring. Berlin.
[9] Hitzler, P. and Seda, A. K. (2000). Dislocated topologies. J. Electron. Eng. 51(12), 37.
[10] Hosseini, A. and Fosner, A. (2019). The Structure of Metric-like Spaces. Sah. Comm. in Math. Analy. (SCMA). 14(1), 159-171.
[11] Hussain, N., Roshan, J. R., Parvaneh, V., and Kadelburg, Z. (2014). Fixed Points of Con- tractive Mappings in bMetricLike Spaces. The Scientific World Journal, 2014(1), 471827.
[12] Ma, Z., Jiang, L. and Sun, H. (2014). C∗-algebra-valued metric space and related fixed point theorems. J. Fixed Point Theory and Appl., 206:111.
[13] Ma, Z. and Jiang, L. (2015). C∗-algebra-valued b-metric space and related fixed point theorems. J. Fixed Point Theory and Appl., 2015(1), 222.
[14] Madadi, M., ORegan, D., Park, C., de la Sen, M. and Saadati, R. (2020). On the Topology Induced by C∗-algebra-valued fuzzy metric space. Mathematics, 8(6), 905.
[15] Maheswari, J. U., Anbarasan, A., Gunaseelan, M., Parvaneh, V. and Bonab, S. H.(2022). Solving an integral equation via C∗-algebra-valued partial b-metrics. J. Fixed Point Theory Algorithms Sci. Eng., 18.
[16] Matthews, S. G. (1994). Partial metric topology. In: Proc. 8th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci., vol. 728, pp. 183-197.
[17] Mlaiki, N., Asim, M., and Imdad, M. (2020). C∗-algebra-valued partial b-metric space and fixed point results with an application. Mathematics, 8(8), 1381.
[18] Murphy, G. J.(1990). C∗-Algebras and Operator Theory. Academic Press, London.
Published
2026-03-09
How to Cite
AHMAD, Z. T., SHAGARI, M. S., YAHAYA, S., & BALARABE, M. (2026). C*-ALGEBRA-VALUED b-METRIC-LIKE SPACE AND SOME FIXED POINT THEOREMS. Unilag Journal of Mathematics and Applications, 6(1), 70 - 84. Retrieved from https://lagjma.unilag.edu.ng/article/view/2871
Section
Articles
Copyright (c) 2026 ZULAIHATU TIJJANI AHMAD, MOHAMMED SHEHU SHAGARI, SIRAJO YAHAYA, MUSA BALARABE
This work is licensed under a Creative Commons Attribution 4.0 International License.
