Common fixed point theorem involving contractive conditions of rational type in dislocated quasi-metric space
Abstract
In this paper, we have proved the existence and uniqueness of a common fixed-point theorem for a finite family of self-mappings involving contractive conditions of Rational type in dislocated quasi-metric spaces by extending and generalizing the result of Jira et al. [10].
Keywords
- fixed point,
- dislocated quasi-metric space,
- weakly compatible mappings,
- coincidence points
References
- C. T. Aage and J. N. Salunke, The results on fixed points in dislocated and dislocated quasi-metric space, Appl. Math. Sci., 2 (2008), 2941–2948.
- C. T. Aage and J. N. Salunke, Some results of fixed point theorem in dislocated quasi-metric spaces, Bull. Marathwada Math. Soc., 9 (2018), 1–5.
- S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133–181.
- V. Berinde, On the approximation of fixed point of weak contractive mapping, Carpath. J. Math., 19 (2003), 7–22.
- S. K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci., 25 (1972), 727–730.
- S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostrav., 1 (1993), 5–11.
- B. K. Dass and S. Gupta, An extension of Banach contraction principles through rational expression, Indian J. Pure Appl. Math., 6 (1975), 1455–1458.
- P. Hitzler and A. K. Seda, Dislocated topologies, J. Electric. Eng., 51 (2000), 3–7.
- A. Isufati, Fixed point theorems in dislocated quasi-metric space, Appl. Math. Sci., 4 (2010), 217–223
- Y. Jira, K. Koyas, and A. Girma, Common fixed point theorems involving contractive conditions of rational type in dislocated quasi metric spaces, Adv. Fixed Point Theory, 8 (2018), 341–366.
- G. Jungck, Commuting mappings and fixed points, Amer. Math. Month., 83 (1976), 261–263.
- G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (1986), 771–779.
- G. Jungck and B. E. Rhoades, Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227–238.
- R. Kannan, Some results on fixed point, Bull. Calcutta Math. Soc., 60 (1968), 71–76
- R. Kannan, Some results on fixed points-II, Amer. Math. Month., 76 (1969), 405–408.
- P. K. B. Prajapati Fixed point theorem of Integral type mapping in Sb-metric space, Math. Anal. Contemp. Appl., 5(4) (2023), 41–53.
- P. K. B. Prajapati and B. Ramakant, Fixed point theorems in bi-b-metric spaces, Math. Anal. Contemp. Appl., 5(3) (2023), 73–81.
- P. K. B. Prajapati, R. Bhardwaj, and P. Bhatnagar, Extension of some common fixed point theorems of integral type mappings in Hilbert space, Network Complex Syst., 4(6) (2014), 1–17.
- M. U. Rahman and M. Sarwar, Fixed point results in dislocated quasi metric spaces, Int. Math. Forum, 9 (2014), 677–682. COMMON FIXED POINT THEOREM INVOLVING CONTRACTIVE CONDITIONS... 21
- M. Sarwar, M. U. Rahman, and G. Ali, Some fixed point results in dislocated quasi metric (dq-metric) spaces, J. Inequal. Appl., 2014 (2014), 1–11.
- S. L. Singh and B. Prasad, Some coincidence theorems and stability of iterative procedures, Comput. Math. Appl., 55 (2008), 2512–2520.
- S. K. Tiwari and P. Vishuw, Dislocated quasi b-metric spaces and new common fixed point results, Int. J. Sci. Adv. Res., 3(7) (2017), 60–64.
- W. A. Wilson, On quasi-metric spaces, Amer. J. Math. 53 (1931), 675–684.
- F. M. Zeyada, G. H. Hassan, and M. A. Ahmed, A generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces, Arab. J. Sci. Eng., 31 (2005), 111–114.
10.30495/maca.2025.2046916.1118