×

Fixed point and common fixed point theorems on ordered cone b-metric spaces. (English) Zbl 1273.54038

Summary: The concept of a cone b-metric space has been introduced recently as a generalization of a b-metric space and a cone metric space in 2011. The aim of this paper is to establish some fixed point and common fixed point theorems on ordered cone b-metric spaces. The proposed theorems expand and generalize several well-known comparable results in the literature to ordered cone b-metric spaces. Some supporting examples are given.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cho, Y. J., Fixed points for compatible mappings of type \((A)\), Mathematica Japonica, 18, 497-508 (1993) · Zbl 0791.54058
[2] Cho, Y. J.; Pathak, H. K.; Kang, S. M.; Jung, J. S., Common fixed points of compatible maps of type \((\beta)\) on fuzzy metric spaces, Fuzzy Sets and Systems, 93, 1, 99-111 (1998) · Zbl 0915.54004 · doi:10.1016/S0165-0114(96)00200-X
[3] Huang, L. G.; 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 · doi:10.1016/j.jmaa.2005.03.087
[4] Jungck, G.; Cho, Y. J.; Murthy, P. P., Compatible mappings of type \((A)\) and common fixed points, Mathematica Japonica, 38, 2, 381-390 (1993) · Zbl 0791.54059
[5] Kaewkhao, A.; Sintunavarat, W.; Kumam, P., Common fixed point theorems of c-distance on cone metric spaces, Journal of Nonlinear Analysis and Application, 2012 (2012) · doi:10.5899/2012/jnaa-00137
[6] Vandergraft, J. S., Newton’s method for convex operators in partially ordered spaces, SIAM Journal on Numerical Analysis, 4, 406-432 (1967) · Zbl 0161.35302 · doi:10.1137/0704037
[7] \'Cirić, L.; Abbas, M.; Saadati, R.; Hussain, N., Common fixed points of almost generalized contractive mappings in ordered metric spaces, Applied Mathematics and Computation, 217, 12, 5784-5789 (2011) · Zbl 1206.54040 · doi:10.1016/j.amc.2010.12.060
[8] 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 · doi:10.1007/s12215-009-0026-y
[9] Altun, I.; Damjanović, B.; Djorić, D., Fixed point and common fixed point theorems on ordered cone metric spaces, Applied Mathematics Letters, 23, 3, 310-316 (2010) · Zbl 1197.54052 · doi:10.1016/j.aml.2009.09.016
[10] Kadelburg, Z.; Pavlović, M.; Radenović, S., Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces, Computers & Mathematics with Applications, 59, 9, 3148-3159 (2010) · Zbl 1193.54035 · doi:10.1016/j.camwa.2010.02.039
[11] Choudhury, B. S.; Metiya, N., Fixed point and common fixed point results in ordered cone metric spaces, Analele Stiintifice ale Universitatii Ovidius Constanta, 20, 1, 55-72 (2012) · Zbl 1274.54120
[12] Shatanawi, W., Partially ordered cone metric spaces and coupled fixed point results, Computers & Mathematics with Applications, 60, 8, 2508-2515 (2010) · Zbl 1205.54044 · doi:10.1016/j.camwa.2010.08.074
[13] Nashine, H. K.; Kadelburg, Z.; Radenović, S., Coupled common fixed point theorems for \(w^*\)-compatible mappings in ordered cone metric spaces, Applied Mathematics and Computation, 218, 9, 5422-5432 (2012) · Zbl 1267.54050 · doi:10.1016/j.amc.2011.11.029
[14] Agarwal, R. P.; Sintunavarat, W.; Kumam, P., Coupled coincidence point and common coupled fixed point theorems lacking the mixed monotone property, Fixed Point Theory and Applications, 2013, article 22 (2013) · Zbl 1295.54039 · doi:10.1186/1687-1812-2013-22
[15] Cho, Y. J.; Saadati, R.; Wang, S., Common fixed point theorems on generalized distance in ordered cone metric spaces, Computers & Mathematics with Applications, 61, 4, 1254-1260 (2011) · Zbl 1217.54041 · doi:10.1016/j.camwa.2011.01.004
[16] Sintunavarat, W.; Cho, Y. J.; Kumam, P., Common fixed point theorems for \(c\)-distance in ordered cone metric spaces, Computers & Mathematics with Applications, 62, 4, 1969-1978 (2011) · Zbl 1231.54028 · doi:10.1016/j.camwa.2011.06.040
[17] Cho, Y. J.; Kadelburg, Z.; Saadati, R.; Shatanawi, W., Coupled fixed point theorems under weak contractions, Discrete Dynamics in Nature and Society, 2012 (2012) · Zbl 1250.54046 · doi:10.1155/2012/184534
[18] Hussain, N.; Shah, M. H., KKM mappings in cone b-metric spaces, Computers & Mathematics with Applications, 62, 4, 1677-1684 (2011) · Zbl 1231.54022 · doi:10.1016/j.camwa.2011.06.004
[19] Aydi, H.; Bota, M.-F.; Karapinar, E.; Mitrović, S., A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory and Applications, 2012, article 88 (2012) · Zbl 1457.54032 · doi:10.1186/1687-1812-2012-88
[20] Cvetković, A. S.; Stanić, M. P.; Dimitrijević, S.; Simić, S., Common fixed point theorems for four mappings on cone metric type space, Fixed Point Theory and Applications, 2011 (2011) · Zbl 1221.54054
[21] Stanić, M. P.; Cvetković, A. S.; Simić, S.; Dimitrijević, S., Common fixed point under contractive condition of Cirics type on cone metric type spaces, Fixed Point Theory and Applications, 2012, article 35 (2012) · Zbl 1273.54077 · doi:10.1186/1687-1812-2012-35
[22] Shah, M. H.; Simić, S.; Hussain, N.; Sretenović, A.; Radenović, S., Common fixed points theorems for occasionally weakly compatible pairs on cone metric type spaces, Journal of Computational Analysis and Applications, 14, 2, 290-297 (2012) · Zbl 1256.54081
[23] Huang, H.; Xu, S., Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory and Applications, 2012, article 220 (2012) · doi:10.1186/1687-1812-2012-220
[24] Jungck, G.; Radenović, S.; Radojević, S.; Rakočević, V., Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory and Applications, 2009 (2009) · Zbl 1190.54032
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.