×

Common fixed point theorems for a pair of self-mappings in fuzzy cone metric spaces. (English) Zbl 1474.54276

Summary: In this paper, we present some common fixed point theorems for a pair of self-mappings in fuzzy cone metric spaces under the generalized fuzzy cone contraction conditions. We extend and improve some recent results given in the literature.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54A40 Fuzzy topology
54E40 Special maps on metric spaces
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606
[2] Kramosil, I.; Michalek, J., Fuzzy metrics and statistical metric spaces, Kybernetika, 11, 5, 326-334 (1975)
[3] George, A.; Veeramani, P., On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64, 3, 395-399 (1994) · Zbl 0843.54014
[4] Hadzic, O.; Pap, E., A fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces, Fuzzy Sets and Systems, 127, 3, 333-344 (2002) · Zbl 1002.54025
[5] Kiany, F.; Amini-Harandi, A., Fixed point and endpoint theorems for set-valued fuzzy contraction maps in fuzzy metric spaces, Fixed Point Theory and Applications, 94 (2011) · Zbl 1312.54025
[6] Sadeghi, Z.; Vaezpour, S. M.; Park, C.; Saadati, R.; Vetro, C., Set-valued mappings in partially ordered fuzzy metric spaces, Journal of Inequalities and Applications, 2014, article 157 (2014) · Zbl 1308.54035
[7] Som, T., Some results on common fixed point in fuzzy metric spaces, Soochow Journal of Mathematics, 33, 4, 553-561 (2007) · Zbl 1137.54308
[8] Pant, R. P., Common fixed points of noncommuting mappings, Journal of Mathematical Analysis and Applications, 188, 2, 436-440 (1994) · Zbl 0830.54031
[9] Som, T., Some fixed point theorems on metric and Banach spaces, Indian Journal of Pure and Applied Mathematics, 16, 6, 575-585 (1985) · Zbl 0581.54027
[10] Vasuki, R., Common fixed points for \(R\)-weakly commuting maps in fuzzy metric spaces, Indian Journal of Pure and Applied Mathematics, 30, 4, 419-423 (1999) · Zbl 0924.54010
[11] Imdad, M.; Ali, J., Some common fixed point theorems in fuzzy metric spaces, Mathematical Communications, 11, 2, 153-163 (2006) · Zbl 1152.54355
[12] Kutukcu, S.; Turkoglu, D.; Yildiz, C., Common fixed points of compatible maps of type \((β)\) on fuzzy metric spaces, Communications of the Korean Society, Communications of the Korean Mathematical Society, 21, 1, 89-100 (2006) · Zbl 1162.54334
[13] Murthy, P. P.; Kumar, S.; Tas, K., Common fixed points of self maps satisfying an integral type contractive condition in fuzzy metric spaces, Mathematical Communications, 15, 2, 521-537 (2010) · Zbl 1213.54069
[14] Pant, B. D.; Chauhan, S., Common fixed point theorems for two pairs of weakly compatible mappings in Menger spaces and fuzzy metric spaces, Scientific Studies and Research. Series Mathematics and Informatics, 21, 2, 81-96 (2011) · Zbl 1289.54143
[15] Sedghi, S.; Turkoglu, D.; Shobe, N., Common fixed point of compatible maps of type \((γ)\) on complete fuzzy metric spaces, Communications of the Korean Mathematical Society, 24, 4, 581-594 (2009) · Zbl 1231.54027
[16] Subrahmanyam, P. V., A common fixed point theorem in fuzzy metric spaces, Information Sciences, 83, 3-4, 109-112 (1995) · Zbl 0867.54017
[17] Huang, L.; Zhang, X., Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications, 332, 2, 1468-1476 (2007) · Zbl 1118.54022
[18] Abbas, M.; Jungck, G., Common fixed point results for noncommuting mappings without continuity in cone metric spaces, Journal of Mathematical Analysis and Applications, 341, 1, 416-420 (2008) · Zbl 1147.54022
[19] Abbas, M.; Rhoades, B. E.; Nazir, T., Common fixed points for four maps in cone metric spaces, Applied Mathematics and Computation, 216, 1, 80-86 (2010) · Zbl 1197.54050
[20] Altun, I.; Damjanovic, B.; Djoric, D., Fixed point and common fixed point theorems on ordered cone metric spaces, Applied Mathematics Letters, 23, 3, 310-316 (2010) · Zbl 1197.54052
[21] Altun, I.; Durmaz, G., Some fixed point theorems on ordered cone metric spaces, Rendiconti del Circolo Matematico di Palermo, 58, 2, 319-325 (2009) · Zbl 1184.54038
[22] Ilić, D.; Rakočević, V., Common fixed points for maps on cone metric space, Journal of Mathematical Analysis and Applications, 341, 2, 876-882 (2008) · Zbl 1156.54023
[23] Ilic, D.; Rakocevic, V., Quasi-contraction on a cone metric space, Applied Mathematics Letters, 22, 5, 728-731 (2009) · Zbl 1179.54060
[24] Radenović, S.; Rhoades, B. E., Fixed point theorem for two non-self mappings in cone metric spaces, Computers & Mathematics with Applications, 57, 10, 1701-1707 (2009) · Zbl 1186.65073
[25] Vetro, P., Common fixed points in cone metric spaces, Rendiconti del Circolo Matematico di Palermo, Serie II, 56, 3, 464-468 (2007) · Zbl 1196.54086
[26] Oner, T.; Kandemir, M. B.; Tanay, B., Fuzzy cone metric spaces, Journal of Nonlinear Sciences and Applications, 8, 5, 610-616 (2015) · Zbl 1328.54007
[27] Rehman, S. U.; Li, H.-X., Fixed point theorems in fuzzy cone metric spaces, Journal of Nonlinear Sciences and Applications. JNSA, 10, 11, 5763-5769 (2017) · Zbl 1412.47181
[28] Ali, A. M.; Kanna, G. R., Intuitionistic fuzzy cone metric spaces and fixed point theorems, International Journal of Applied Mathematics, 5, 25-36 (2017)
[29] Oner, T., On some results in fuzzy cone metric spaces, International Journal of Computer Science and Network, 4, 37-39 (2016)
[30] Oner, T., On the metrizability of fuzzy cone metric spaces, International Journal of Management and Applied Science, 2, 133-135 (2016)
[31] Oner, T., Some topological properties of fuzzy cone metric spaces, Journal of Nonlinear Sciences and Applications, 9, 3, 799-805 (2016) · Zbl 1328.54006
[32] Schweizer, B.; Sklar, A., Statistical metric spaces, Pacific Journal of Mathematics, 10, 313-334 (1960) · Zbl 0091.29801
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.