Common fixed point for pairs of weakly compatible mappings in C*-algebra valued b-metric space
DOI:
https://doi.org/10.5269/bspm.66142Resumo
In this article, we vouched for some results on common fixed points for two pairs of weakly compatible mappings with a generalized contractive condition satisfying $(E.A.)$ and $(CLR)$ properties in the framework of $C^*$-algebra valued $b$-metric spaces. The proven results extend and generalize some of the results in the literature. To verify the confirmed results, we demonstrated some examples.
Referências
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12. S. K. Mohanta, Common fixed point results in C∗-algebra valued b-metric spaces via digraphs, Cubo., 20 (2018), 41-64.
13. S. Mondal, A. Chanda, S. Karmakar, Common fixed point and best proximity point theorems in C∗-algebra valued metric space, Int. J. Pure Appl. Math., 115 (2017), 477-496.
14. S. Radenovic, P. Vetro, A. Nastasi, L. T. Quan, Coupled fixed point theorems in C∗-algebra valued b-metric spaces, Publ. State Univ. Novi Pazar, Ser. A Appl. Math. Inform. Mech., 9 (2017), 81-90.
15. S. Omran, I. Masmali, On the α-ψ-contractive mapping in C∗-algebra valued b-metric space, J. Math., Article ID 7865976, 6 pages. https://doi.org/10.1155/2021/7865976
16. W. Sintunavarat, P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., (2011), Article ID 637958, 14 pages. https://doi.org/10.1155/2011/637958
17. X. Qiaoling, J. Lining, Z. Ma, Common fixed point theorem in C∗-algebra valued metric space, arXiv : 1506.05545v2, (2015). https:/links/567caec308aebccc4e012341/Common-fixed-point-theorems-in-C-algebra-valued-metric-spaces.pdf
18. Z. Ma, L. Jiang, H. Sun, C∗ -algebra valued metric spaces and related fixed point theorems, Fixed Point Theory Appl., 206 (2014). http://www.fixedpointtheoryandapplications.com/content/2014/1/206
19. Z. Ma, L. Jiang, C∗ -algebra valued b-metric spaces and related fixed point theorems, Fixed Point Theory Appl., 222 (2015). DOI 10.1186/s13663-015-0471-6
2. B. Moeini, P. Kumar, H. Aydi, Zamfirescu type contraction on C∗-algebra valued metric space, J. Math. Anal., 9 (2018), 150-161.
3. D. Kumar, D. Rishi, C. Park, J. R. Lee, On fixed point in C∗-algebra valued metric spaces using C∗-class function, Int. J. Nonlinear Anal. Appl., 12 (2021), 1157-1161.
4. H. Massit, M. Rossafi, Fixed point theorem for (ϕ, F )-contraction on C∗-algebra valued metric space, Eur. J. Math. Appl., 1 (2021). http://ejma.euap.org
5. M. Asim, R. George, M. Imdad, Suzuki type multivalued contractions in C∗-algebra valued metric spaces with an application, AIMS Math., 6 (2020), 1126–1139.
6. M. Kumar, M. Imdad, M. Asim, Some fixed point theorems under E.A. and (CLR) properties on C∗-algebra valued metric spaces, Inf. Sci. Lett., 9 (2020), 75-82.
7. M. Rossafi, H. Massit, S. Kabbaj, Fixed point theorem for (ϕ, MF )-contraction on C∗algebra valued metric space, Asian J. Math. Appl., 7 (2022). https://scienceasia.asia/files/2022-7.pdf
8. M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188.
9. N. Mlaiki, M. Asim, M. Imdad, C∗-algebra valued partial b-metric spaces and fixed point results with an application, J. Math., 8, (2020). https:// pdfs.semanticscholar.org/5eb1/fa06d7d7db5f7b41d0c74b7ac9fa8472c0a5
10. N. V. Dung, V.T.L. Hang, D. D-Djekic, An equivalence of resluts in C∗-algebra valued b-metric and b-metric space, Appl. Gen. Topo., 18 (2017), 241-253.
11. S. Chandok, D. Kumar, C. Park, C∗-algebra valued partial metric space and fixed point theorems, Proc. Math. Sci., 129 (2019). DOI: 10.1007/s12044-019-0481-0
12. S. K. Mohanta, Common fixed point results in C∗-algebra valued b-metric spaces via digraphs, Cubo., 20 (2018), 41-64.
13. S. Mondal, A. Chanda, S. Karmakar, Common fixed point and best proximity point theorems in C∗-algebra valued metric space, Int. J. Pure Appl. Math., 115 (2017), 477-496.
14. S. Radenovic, P. Vetro, A. Nastasi, L. T. Quan, Coupled fixed point theorems in C∗-algebra valued b-metric spaces, Publ. State Univ. Novi Pazar, Ser. A Appl. Math. Inform. Mech., 9 (2017), 81-90.
15. S. Omran, I. Masmali, On the α-ψ-contractive mapping in C∗-algebra valued b-metric space, J. Math., Article ID 7865976, 6 pages. https://doi.org/10.1155/2021/7865976
16. W. Sintunavarat, P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., (2011), Article ID 637958, 14 pages. https://doi.org/10.1155/2011/637958
17. X. Qiaoling, J. Lining, Z. Ma, Common fixed point theorem in C∗-algebra valued metric space, arXiv : 1506.05545v2, (2015). https:/links/567caec308aebccc4e012341/Common-fixed-point-theorems-in-C-algebra-valued-metric-spaces.pdf
18. Z. Ma, L. Jiang, H. Sun, C∗ -algebra valued metric spaces and related fixed point theorems, Fixed Point Theory Appl., 206 (2014). http://www.fixedpointtheoryandapplications.com/content/2014/1/206
19. Z. Ma, L. Jiang, C∗ -algebra valued b-metric spaces and related fixed point theorems, Fixed Point Theory Appl., 222 (2015). DOI 10.1186/s13663-015-0471-6
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2025-07-12
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Dhariwal, R., & Kumar, D. D. (2025). Common fixed point for pairs of weakly compatible mappings in C*-algebra valued b-metric space. Boletim Da Sociedade Paranaense De Matemática, 43, 1-15. https://doi.org/10.5269/bspm.66142
