Common Fixed Point Theorems For Weakly Compatible Mappings Satisfying Rational Contractive Conditions
DOI:
https://doi.org/10.61841/41qg3a85Keywords:
Complete metric spaces,, fixed points,, compatible mapping, weak compatible mapping.Abstract
By using notions of compatibility, weak compatibility and commutativity, we prove some common fixed point theorems for six mappings involving rational contractive conditions motivated by Nesic [13] in complete metric spaces. Our work generalizes some earlier results of Fisher [1], Jeong-Rhoades [6], Kannan [11] and others.
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References
B. Fisher., “Mappings satisfying on fixed points”, Bull. Cal. Math. Soc., 60 (1968), 71-76.
[2]. B. Fisher, “Common fixed point and constant mapping satisfying a rational inequality”, Math. Sem. Notes., 6 (1978), 29-35.
[3]. B. Fisher., “Mapping satisfying rational inequality”, Nanta. Math., 12 (1979), 195-199.
[4]. Lj. Gajic., “On common fixed point of compatible mappings of type (A) on metric and 2-metric spaces”, Filomat (Nis)., 10 (1996), 177-186.
[5]. A. K. Goyal, “Common fixed point theorem for six mappings in complete metric spaces”, Bull. Pure Appl. Math., 3 (1), 24–35, 2009.
[6]. G.S. Jeong and B.E. Rhoades., “Some remarks for improving fixed point theorem for more than two maps”, Ind. J. Pure. Appl. Math 28 (9) (1997), 1177-1196.
[7]. G. Jungck and B.E. Rhoades., “Fixed point for set valued function without continuity”, Ind. J. Pure. Appl. Math., 29
(3) (1998), 227-238.
[8]. J. Jungck., “Compatible mappings and common fixed point”, Internet. J. Math and Math. Sci., 9 (4) (1986), 771-779. [9]. G. Jungck., “Commuting mappings and fixed points”, Amer. Math. Monthly., 83 (1976), 261-263.
[10]. J. Jungck, P.P. Murthy and Y.J. Cho., “Compatible mapping of type (A) and common fixed point theorems”, Math.
Japon., 38 (2) (1993), 381-390.
[11]. R. Kannan., “Some results on fixed point”, Bull. Cal. Math. Soc., 60 (1968), 71-76. [12]. R. Kannan., “Some results in fixed points”, Amer. Math. Monthly., 76 (1969), 405-408.
[13]. Slobodan, C. Nesic., “Results on fixed points of aymptotically regular mappings”, Ind. J. Pure. Appl. Math., 30 (5) (1999), 491-494.
[14]. S. Sessa., “On a weak commutativity condition in fixed point consideration”, Publ. Inset. Math., 32 (1982), 149-153.
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