Some new coincidence point results in partial $b$-metric spaces via digraphs, $\mathscr{L}$-simulation and $\theta$-functions

[1] M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008), 416–420.

[2] J. Ahmad, A.E. Al-Mazrooei, Y.J. Cho, and Y.O. Yang, Fixed point results for generalized θ-contractions, J. Nonlinear Sci. Appl. 10 (2017), 2350–2358.

[3] Anuradha and S. Mehra, Fixed point results using implicit relation on partial b-metric spaces endowed with a graph, AIP Conf. Proc. 2357 (2022).

[4] M. Aphane, S. Moshokoa, and F. Ncongwane, On the 0-Cauchy completion of a partial b-metric space, Q. Math. 46 (2023), 1743–1750.

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

[6] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. 3 (1922), 133–181.

[7] F. Bojor, Fixed point of φ-contraction in metric spaces endowed with a graph, Ann. Univ. Cralova, Math. Comput. Sci. Ser. 37 (2010), 85–92.

[8] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, American Elsevier Publishing Co., Inc., New York, 1976.

[9] G. Chartrand, L. Lesniak, and P. Zhang, Graph and digraph, CRC Press, New York, NY, USA, 2011.

[10] S.H. Cho, Fixed point theorems for L -contractions in generalized metric spaces, Abstr. Appl. Anal. 2018 (2018), Article ID 1327691, 6 pages.

[11] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostrav 1 (1993), 5–11.

[12] N.V. Dung and V.T.L. Hang, Remarks on partial b-metric spaces and fixed point theorems, Mate. Vesnik 69 (2017), 231–240.

[13] F. Echenique, A short and constructive proof of Tarski’s fixed point theorem, Int. J. Game Theory 33 (2005), 215–218.

[14] R. Espinola and W.A. Kirk, Fixed point theorems in R-trees with applications to graph theory, Topol. Appl. 153 (2006), 1046–1055.

[15] A. Farajzadeh, M. Delfani, and S. Suantai, A modification of simulation function and its applications to fixed point theory, Thai J. Math. 20 (2022), 1471–1477.

[16] A. Farajzadeh, M. Delfani, and Y.H. Wang, Existence and uniqueness of fixed points of generalized F-contraction mappings, J. Math. 2021 (2021), Article ID 6687238, 9 pages.

[17] X. Ge and S. Lin, A note on partial b-metric spaces, Mediterr. J. Math. 13 (2016), 1273–1276.

[18] J.I. Gross and J. Yellen, Graph Theory and its Applications, CRC Press, New York, NY, USA, 1999.

[19] P. Hitzler and A.K. Seda, Dislocated topologies, J. Electron. Eng. 51 (2000) 3–7.

[20] M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014 (2014), 8 pages.

[21] G. Jungck, Common fixed points for noncontinuous non-self maps on non-metric spaces, Far East J. Math. Sci. 4 (1996), 199–215.

[22] F. Khojasteh, S. Shukla, and S. Radenovic, A new approach to the study of fixed point theorems via simulations, Filomat 29 (2015), 1189–1194.

[23] U. Maheswari, M. Ravichandran, A. Anbarasan, L. Rathour, and V.N. Mishra, Some results on coupled fixed point on complex partial b-metric space, GANITA 71 (2021), 17–27.

[24] S. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci. 728 (1994), 183–197.

[25] S.K. Mohanta, Common fixed points in b-metric spaces endowed with a graph, Math. Vesnik 68 (2016), 140–154.

[26] S.K. Mohanta, Some fixed point theorems using wt-distance in b-metric spaces, Fasciculi Math. 54 (2015), 125–140.

[27] S. Moshokoa and F. Ncongwane, On completeness in strong partial b-metric spaces, strong b-metric spaces and the 0-Cauchy completions, Topol. Appl. 275 (2020), 107011.

[28] G.S. Saluja, Coupled fixed point results for contractive type conditions in partial b-metric spaces, Annals Math. Comp. Sci. 14 (2023), 12–28

[29] S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math. 11 (2014), 703–711.