COMMON FIXED POINT RESULTS FOR W-COMPATIBLE MAPPINGS ALONG WITH CLRST PROPERTY IN FUZZY METRIC SPACES

Yıl 2019, Cilt: 9 Sayı: 4, 851 - 863, 01.12.2019

M. Jain N. Gupta S. Kumar

Öz

In this paper, we extend the concepts of common property E.A and CLRST property for problems in coupled xed point theory. Employing these notions, we prove some common xed point results for the pairs of w-compatible mappings subjected to  { contractions in fuzzy metric spaces and generalize and extend some results present in the literature.

Anahtar Kelimeler

Common property E.A., CLRST property, metric space, fuzzy metric space, w-compatible mappings, common xed points

Kaynakça

• Aamri, M. and El-Moutawakil, D., (2002), Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 27, pp. 181-188.
• Abbas, M., Altun, I. and Gopal, D., (2009), Common fixed point theorems for non compatible map- pings in fuzzy metric spaces, Bull. Math. Anal. Appl., 1 (2), pp. 47-56.
• Abbas, M., Ali Khan, M. and Radenovi´c, S., (2010), Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., 217 (1), pp. 195-202.
• Bhaskar, T.G. and Lakshmikantham, V., (2006), Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (7), pp. 1379-1393.
• Chauhan, S., Sintunavarat, W. and Kumam, P., (2012), Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property, Applied Mathematics, 3 (9), pp. 976-982.
• Chauhan, S., (2012), Fixed points of weakly compatible mappings in fuzzy metric spaces satisfying common limit in the range property, Indian J. Math., 54 (3), pp. 375-397.
• Guo, D. and Lakshmikantham, V., (1987), Coupled fixed points of nonlinear operators with applica- tions, Nonlinear Anal., 11 (5), pp. 623-632.
• Grabiec, M., Fixed points in fuzzy metric spaces, (1988), Fuzzy Sets and Systems, 27 (3), pp. 385-389. [9] George, A. and Veeramani, P., (1994), On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (3), pp. 395-399.
• Gupta, V., Saini, R.K. and Kanwar, A., (2016), Some Common Coupled Fixed Point Results on Modified Intuitionistic Fuzzy Metric Spaces, Procedia Computer Science, 79, pp. 32-40.
• Hu, X.Q., (2011), Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces, Fixed Point Theory Appl., 2011: Article ID 363716, 14 pages.
• Hu, X.Q., Zheng, M.X., Damjanovi´c, B. and Shao X.F., (2013), Common coupled fixed point theorems for weakly compatible mappings in fuzzy metric spaces, Fixed Point Theory Appl., 2013, 2013: 220.
• Had˘zi´c, O. and Pap, E., (2001), Fixed Point Theory in Probabilistic Metric Spaces, Vol. 536 of Mathematics and its Applications, Kluwer Academic, Dordrecht, The Netherlands.
• Jain, M., Tas, K., Kumar, S. and Gupta, N., (2012), Coupled Fixed Point Theorems for a Pair of Weakly Compatible Maps along with CLRg Property in Fuzzy Metric Spaces, J. Appl. Math., 2012: Article ID 961210, 13 pages. doi:10.1155/2012/961210
• Jain, M., Kumar, S. and Chugh, R., (2013), Coupled fixed point theorems for weak compatible mappings in fuzzy metric spaces, Ann. Fuzzy Math. Inform., 5 (2), pp. 321-336.
• Kramosil, I. and Michalek, J., (1975), Fuzzy Metric and Statistical Metric Spaces, Kybernetika, 11, pp. 326-334.
• Lakshmikantham, V. and ´Ciri´c, Lj. B., (2009), Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70, pp. 4341-4349.
• Liu, Y., Wu, J. and Li, Z., (2005), Common fixed points of single-valued and multivalued maps, Int. J. Math. Math. Sci., vol. 2005, no. 19, pp. 3045-3055.
• Rodr´ıguez L´opez, J. and Romaguera, S., (2004), The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems, 147, pp. 273-283.
• Sedghi, S., Altun, I. and Shobe, N., (2010), Coupled fixed point theorems for contractions in fuzzy metric spaces, Nonlinear Anal., 72 (3), pp. 1298-1304.
• Sintunavarat, W. and Kumam, P., (2011), Common fixed point theorems for a pair of weakly com- patible mappings in Fuzzy Metric Spaces, J. Appl. Math., 2011: Article ID 637958, 14 pages. doi: 10.1155/2011/637958.
• Schweizer, B. and Sklar, A., (1983), Probabilistic Metric Spaces, North Holland Series in Probability and Applied Math, 5.
• Zadeh, L.A., (1965), Fuzzy Sets, Information and Control, 89, pp. 338-353.