Common fixed point results via $F$-contraction on $C^{\ast}$-algebra valued metric spaces
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Abstract
In this work, we establish common fixed point results by utilizing a variant of $F$-contraction in the framework of $C^{\ast}$-algebra valued metric spaces. We utilize E.A. and C.L.R. property possessed by the mappings to prove common fixed point results in the same metric settings. To validate the applicability of these common fixed point results, we provide illustrative examples too.
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References
[1] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fund. Math. 3 (1922), 133–181. Google Scholar
[2] S.G. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci. 728 (1994 ), 183–197. Google Scholar
[3] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Univ. Ostrav. 1 (1993), 5–11. Google Scholar
[4] 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
[5] M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008), 416–420. Google Scholar
[6] J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Am. Math. Soc. 136 (4), (2008), 1359–1373. Google Scholar
[7] Y. J. Cho, R. Saadati, S. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl., 61 (2011), 1254–1260. Google Scholar
[8] R.C. Dimri, G. Prasad, Coincidence theorems for comparable generalized non-linear contractions in ordered partial metric spaces, Commun. Korean Math. Soc. 32 (2) (2017), 375–387. Google Scholar
[9] G. Prasad, Fixed point theorems via w-distance in relational metric spaces with an application, Filomat 34(6) (2020), 1889–1898. Google Scholar
[10] G. Prasad, R.C. Dimri, A. Bartwal, Fixed points of Suzuki contractive mappings in relational metric spaces, Rend. Circ. Mat. Palermo, Ser II 69 (2020), 1347–1358. https://doi.org/10.1007/s12215-019-00475-4 Google Scholar
[11] G. Prasad, D. Khantwal, Fixed points of JS-contractive mappings with applications, J. Anal. (2023). https://doi.org/10.1007/s41478-023-00598-z Google Scholar
[12] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012,94, (2012). Google Scholar
[13] D. Wardwoski, N. V. Dung, Fixed points of F-weak contraction on complete metric spaces, Demonstr. Math. 47 (2014). Google Scholar
[14] D. Klim, D. Wardowski, Fixed points of dynamic processes of set-valued F contractions and application to functional equations, Fixed Point Theory Appl. 2015, 22, (2015). Google Scholar
[15] I. Altun, G. Minak, H. Dag, Multivalued F-contractions on complete metric spaces, J. Nonlinear Convex Anal. 16 (2015), 659–666. Google Scholar
[16] M. Nazam, C. Park, A. Hussain, M. Arshad, J. R. Lee, Fixed point theorems for F -contractions on closed ball in partial metric spaces, J. Comput. Anal. Appl. 27 (2019), 759–769. Google Scholar
[17] Z.H. Ma, L.N. Jiang, H.K. Sun, C∗-algebra valued metric spaces and related fixed point theorems, Fixed Point Theory Appl. 2014, 206, (2014). Google Scholar
[18] Z.H. Ma, L.N. Jiang, C∗-algebra valued b-metric spaces and related fixed point theorems, Fixed Point Theory Appl. 2015, 222, (2015). https://doi.org/10.1186/s13663-015-0471-6 Google Scholar
[19] M.E. Ege, C. C. Alaca, C∗-algebra-valued S-metric spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 67 (2) (2018), 165–177. Google Scholar
[20] N. Mlaike, M. Asim, M. Imdad, C∗-algebra valued partial b-metric spaces and fixed point results with an application, Mathematics 8 (8), (2020). https://doi.org/10.3390/math8081381 Google Scholar
[21] J.U. Maheswari, A. Anbarasan, M. Gunaseelan, V. Parvaneh, H. Bonab, Solving an integral equation via C∗-algebra-valued partial b-metrics, Fixed Point Theory Algorithms Sci Eng 2022, 18 (2022). Google Scholar
[22] W. Tapanyo, W. Ratiphaphongthon, A. Arunchai, Completion of C∗-algebra-valued metric spaces, Thai J. Math., 20 (3), (2022), 1119–1136. Google Scholar
[23] G. Mani, A.J. Gnanaprakasam, O. Ege, A. Aloqaily, N. Mlaiki, Fixed point results in C∗-algebra-valued partial b-metric spaces with related application, Mathematics 11 (5), 1158, (2023) 1–9. Google Scholar
[24] M. Paul, K. Sarkar, K. Tiwary, Some unique common fixed point results on C∗-algebra valued metric space using C∗-class function, Ann. Math. Comput. Sci. 16, (2023), 1–20. Google Scholar
[25] S. Narzary, D. Das, Y.M. Singh, M.S. Khan, S. Sessa, C∗-algebra-valued partial modular metric spaces and some fixed point results, Symmetry 15 (6), 1135, (2023). Google Scholar
[26] X. Qiaoling, J. Lining, Z. Ma, Common fixed point theorems in C∗-algebra valued metric spaces, J. Nonlinear Sci. Appl. 9 (2016), 4617–4627. Google Scholar
[27] D. El. Moutawakil, M. Aamri, Some new common fixed point theorems under strict contraction conditions, J. Math. Anal. Appl. 270 (2002), 181–188. Google Scholar
[28] P. Kumam, W. Sintunavarat, Common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space, J. Appl. Math. 2011 (2011). https://doi.org/10.1155/2011/637958 Google Scholar
[29] K. Goebel, A coincidence theorem, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 16 (1968), 733–735. Google Scholar
[30] G. Jungck, B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (3), (1998), 227–238. Google Scholar