Volume 65 | Issue 4 | Year 2019 | Article Id. IJMTT-V65I4P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I4P513
The main purpose of this paper is to prove some fixed point results for mappings satisfying various contractive conditions on Complete G−Metric spaces. We also prove the uniqueness of such fixed points as well as we showed these mappings are G-continuous on such fixed points.
[1] Abbas M., Rhoades,B.E., Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Appl. Math. Comput., (2009).
[2] Choudhury,B.S., Maity, P., Coupled fixed point results in generalized metric spaces, Math. Comput. Modelling, 54 (2011),73-79.
[3] Dehghan Nezhad, A. and H. Mazaheri, New results in G-best approximation in Gmetric spaces, Ukrainian Math. J. 62 (2010)648-654.
[4] Dhage, B.C., Generalized metric space and mapping with fixed points, Bulletin of theCalcutta Mathematical Society, 84 (1992), 329-336.
[5] Dhage, B.C., Generalized metric spaces and topological structure - I, Analete Stiintifice ale Universitatii. “Al. I. Cuza” dina Iasi. Serie Nova, Mathametical, 46, No. 1 (2000), 3-24.
[6] G¨ahler, S., 2-metriche Raume undihre topologische struktur, Mathematische Nachrichten, 26, No. 1-4 (1963), 115-148.
[7] Hassen Aydi, W. Shatanawi and Calogero Vetro, on generalized weakly G-contraction mapping in G-metric Spaces, Comput.Math. Appl. 62 (2011) 4222-4229.
[8] Kada, O., Suzuki,T., Takahashi,W., Nonconvex minimization theorems and fixed point theorems in complete metric spaces,Math. Japon. 44 (1996) 381-391.
[9] Mustafa, Z. and B. Sims, 2006. A new approach to generalized metric spaces. J. Nonlinear Convex Anal., 7: 289-297.
[10] Mustafa,Z., Obiedat,H., and Awawdeh,F., Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theoryand Applications, Volume 2008, Article ID 189870.
[11] Mustafa,Z., Shatanawi ,W., Bataineh,M., Fixed point theorem on uncomplete G-metric spaces, Journal of Mathematics and Statistics, 4 (2008), 196-201.
[12] Mustafa,Z., Shatanawi ,W.,andBataineh,M., , Existence of fixed point results in G-metric spaces, Int. J. of Math. and Math. Sci.,Volume 2009, Article ID 283028, doi:10.1155/2009/28302.
[13] Mustafa, Z. and B. Sims,fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory and Applications, Volume 2009, Article ID 917175.
[14] Saadati, A., Vaezpour, S.M., Vetro, P., and B.E. Rhoades, Fixed Point Theorems in generalized partially ordered G-metric spaces, Math. Comput. Modelling 52 (2010) 797-801.
[15] Shatanawi, W., Some Fixed Point Theorems in Ordered G-Metric Spaces and Applications, Abst. Appl. Anal. 2011 (2011) ArticleID 126205.
Anil Rajput, Rucha Athaley, Dharmendra Rajput, "Fixed Point Theorems in Complete G - Metric Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 4, pp. 69-73, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I4P513