Common fixed point results of Das-Naik and Geraghty types in $\boldsymbol{\nu}$-generalized metric spaces
DOI:
https://doi.org/10.5644/SJM.13.1.07Keywords:
v-generalized metric space, common fixed point, Das-Naik- type contraction, Geraghty-type contractionAbstract
In this paper, common fixed point results in $\nu$-generalized metric spaces of Branciari are deduced under several types of contractive conditions.
Downloads
References
M. Abtahi, Z. Kadelburg and S. Radenović, Fixed points of Ćirić-Matkowski-type contractions in $nu$-generalized metric spaces, Rev. Real Acad. Cienc. Exac., Fis. Nat., Ser. A, Mat., DOI:10.1007/s13398-016-0275-5.
B. Alamri, T. Suzuki and L. A. Khan, Caristi's fixed point theorem and Subrahmanyam's fixed point theorem in $nu$-generalized metric spaces, J. Function Spaces, 2015, Art. ID 709391 (2015), 6 pp.
H. Aydi, E. Karapinar, H. Lakzian, Fixed point results on a class of generalized metric spaces, Math. Sci., 6 Art. 46 (2012).
A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31--37.
Lj. B. Ćirić, A new fixed-point theorem for contractive mappings, Publ. Inst. Math. (N.S), 30 (44) (1981), 25--27.
K. M. Das and K. V. Naik, Common fixed point theorems for commuting maps on metric spaces, Proc. Amer. Math. Soc., 77 (1979), 369--373.
M. Geraghty, On contractive mappings}, Proc. Amer. Math. Soc., 40 (1973), 604--608.
Z. Kadelburg and S. Radenović, On generalized metric spaces: A survey, TWMS J. Pure Appl. Math., 5 (2014), 3--13.
Z. Kadelburg and S. Radenović, Fixed point results in generalized metric spaces without Hausdorff property, Math. Sci., 8 Art. 125 (2014).
W. A. Kirk and N. Shahzad, Generalized metrics and Caristi's theorem, Fixed Point Theory Appl., 2013 Art. 129 (2013).
W. A. Kirk and N. Shahzad, Corrections: Generalized metrics and Caristi's theorem, Fixed Point Theory Appl., 2014 Art.177 (2014).
B. Samet, Discussion on A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces' by A. Branciari, Publ. Math. Debrecen, 76 (2010), 493--494.
I. R. Sarma, J. M. Rao and S. S. Rao, Contractions over generalized metric spaces, J. Nonlinear Sci. Appl., 2 (2009), 180--182.
T. Suzuki, Generalized metric spaces do not have the compatible topology, Abstr. Appl. Anal., 2014, Art. ID 458098 (2014), 5 pp.
T. Suzuki, B. Alamri and L.A. Khan, Some notes on fixed point theorems in $nu$-generalized metric spaces, Bull. Kyushu Inst. Tech. Pure Appl. Math., 62 (2015), 15--23.
T. Suzuki, B. Alamri and M. Kikkawa, Only $3$-generalized metric spaces have a compatible symmetric topology, Open Math., 13 (2015), 510--517.
T. Suzuki, B. Alamri, M. Kikkawa, Edelstein's fixed point theorem in generalized metric spaces, J. Nonlinear Convex Anal., 16 (11) (2015), 2301--2309.
T. Suzuki and H. K. Pathak, Almost biased mappings and almost compatible mappings are equivalent under some conditions, J. Math. Anal. Appl., 368 (2010), 211--217.
M. Turinici, Functional contractions in local Branciari metric spaces, Romai J., 8 (2012), 189--199.