On generalized weakly \(G\)-contraction mapping in \(G\)-metric spaces. (English) Zbl 1236.54036
Summary: We establish some common fixed point results for two self-mappings \(f\) and \(g\) on a generalized metric space \(X\). To prove our results we assume that \(f\) is a generalized weakly \(G\)-contraction mapping of types \(A\) and \(B\) with respect to \(g\).
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
References:
| [1] | Gahler, S., 2-Metrische Raume and ihre Topologische Struktur, Math. Nachr., 26, 115-148 (1963) · Zbl 0117.16003 |
| [2] | Gahler, S., Zur Geometric 2-Metrische Raume, Rev. Roumaine Math. Pures Appl., 11, 665-667 (1966) · Zbl 0158.20402 |
| [3] | Dhage, B. C., Generalized metric space and mapping with fixed point, Bull. Calcutta Math. Soc., 84, 329-336 (1992) · Zbl 0782.54037 |
| [4] | Mustafa, Z.; Sims, B., A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7, 289-297 (2006) · Zbl 1111.54025 |
| [5] | Abbas, M.; Khan, A. R.; Nazir, T., Coupled common fixed point results in two generalized metric spaces, Appl. Math. Comput., 217, 6328-6336 (2011) · Zbl 1210.54048 |
| [6] | Abbas, M.; Rhoades, B. E., Common fixed point results for noncommuting mapping without continuity in generalized metric spaces, Appl. Math. Comput., 215, 262-269 (2009) · Zbl 1185.54037 |
| [7] | Aydi, H.; Damjanović, B.; Samet, B.; Shatanawi, W., Coupled fixed point theorems for nonlinear contractions in partially ordered \(G\)-metric spaces, Mathematical and Computer Modelling, 54, 2443-2450 (2011) · Zbl 1237.54043 |
| [8] | Choudhury, B. S.; Maity, P., Coupled fixed point results in generalized metric spaces, Math. Comput. Modelling (2011) · Zbl 1225.54016 |
| [9] | Chugh, R.; Kadian, T.; Rani, A.; Rhoades, B. E., Property \(P\) in \(G\)-metric spaces, Fixed Point Theory Appl., 2010 (2010), ID 401684, 12 pages · Zbl 1203.54037 |
| [10] | Dehghan Nezhad, A.; Mazaheri, H., New results in \(G\)-best approximation in \(G\)-metric spaces, Ukrainian Math. J., 62, 648-654 (2010) · Zbl 1224.41095 |
| [11] | Gajić, L.; Crvenković, Z. L., A fixed point result for mappings with contractive iterate at a point in \(G\)-metric spaces, Filomat, 25, 53-58 (2011) · Zbl 1289.54124 |
| [12] | Gajić, L.; Crvenković, Z. L., On mappings with contractive iterate at a point in generalized metric spaces, Fixed Point Theory Appl., 2010 (2010), Article ID 458086, 16 pages · Zbl 1206.54044 |
| [13] | Z. Mustafa, B. Sims, Some remarks concerning \(D\); Z. Mustafa, B. Sims, Some remarks concerning \(D\) · Zbl 1079.54017 |
| [14] | Mustafa, Z.; Shatanawi, W.; Bataineh, M., Existence of fixed point results in \(G\)-metric spaces, Int. J. Math. Math. Sci., 2009 (2009), Article ID 283028, 10 pages · Zbl 1179.54066 |
| [15] | Mustafa, Z.; Obiedat, H.; Awawdeh, F., Some common fixed point theorem for mapping on complete \(G\)-metric spaces, Fixed Point Theory Appl., 2008 (2008), Article ID 189870, 12 pages · Zbl 1148.54336 |
| [16] | Mustafa, Z.; Khandaqji, M.; Shatanawi, W., Fixed point results on complete \(G\)-metric spaces, Studia Sci. Math. Hungar., 48, 304-319 (2011) · Zbl 1249.54084 |
| [17] | Öztürk, M.; Başarir, M., On some common fixed point theorems with \(\phi \)-maps on \(G\)-cone metric spaces, Bull. Math. Anal. Appl., 3, 121-133 (2011) · Zbl 1314.47093 |
| [18] | Saadati, R.; Vaezpour, S. M.; Vetro, P.; Rhoades, B. E., Fixed point theorems in generalized partially ordered \(G\)- metric spaces, Math. Comput. Modelling, 52, 797-801 (2010) · Zbl 1202.54042 |
| [19] | Shatanawi, W., Fixed point theory for contractive mappings satisfying \(\Phi \)-maps in \(G\)-metric spaces, Fixed Point Theory Appl., 2010 (2010), Article ID 181650, 9 pages · Zbl 1204.54039 |
| [20] | Shatanawi, W., Some fixed point theorems in ordered \(G\)-metric spaces and applications, Abstr. Appl. Anal., 2011 (2011), Article ID 126205, 11 pages · Zbl 1217.54057 |
| [21] | Shatanawi, W., Coupled fixed point theorems in generalized metric spaces, Hacet. J. Math. Stat., 40, 441-447 (2011) · Zbl 1230.54047 |
| [22] | Choudhury, B. S., Unique fixed point theorem for weakly \(C\)-contractive mappings, Kathmandu Univ. J. Sci. Eng. Technol., 5, 1, 6-13 (2009) |
| [23] | Harjani, J.; López, B.; Sadarangani, K., Fixed point theorems for weakly \(C\)-contractive mappings in ordered metric spaces, Comput. Math. Appl., 61, 790-796 (2011) · Zbl 1217.54046 |
| [24] | Shatanawi, W., Fixed point theorems for nonlinear weakly \(C\)-contractive mappings in metric spaces, Math. Comput. Modelling, 54, 2816-2826 (2011) · Zbl 1235.54054 |
| [25] | W. Shatanawi, M. Abbas, H. Aydi, On weakly \(C\); W. Shatanawi, M. Abbas, H. Aydi, On weakly \(C\) |
| [26] | Khan, M. S.; Swaleh, M.; Sessa, S., Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30, 1-9 (1984) · Zbl 0553.54023 |
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