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Jiang, Binghua; Xu, Shaoyuan; Shi, Lu

Coupled coincidence points for mixed monotone random operators in partially ordered metric spaces. (English) Zbl 1469.54122

Abstr. Appl. Anal. 2014, Article ID 484857, 9 p. (2014).
Summary: The aim of this work is to prove some coupled random coincidence theorems for a pair of compatible mixed monotone random operators satisfying weak contractive conditions. These results are some random versions and extensions of results of E. Karapınar et al. [Arab. J. Math. 1, No. 3, 329–339 (2012; Zbl 1253.54044)]. Our results generalize the results of W. Shatanawi and Z. Mustafa [Mat. Vesn. 64, No. 2, 139–146 (2012; Zbl 1289.54160)].

Cited in 2 Documents

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

Citations:

Zbl 1253.54044; Zbl 1289.54160
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References:

[1] Itoh, S., A random fixed point theorem for a multivalued contraction mapping, Pacific Journal of Mathematics, 68, 1, 85-90 (1977) · Zbl 0335.54036 · doi:10.2140/pjm.1977.68.85
[2] Lin, T.-C., Random approximations and random fixed point theorems for non-self-maps, Proceedings of the American Mathematical Society, 103, 4, 1129-1135 (1988) · Zbl 0676.47041 · doi:10.2307/2047097
[3] Abbas, M.; Hussain, N.; Rhoades, B. E., Coincidence point theorems for multivalued \(f\)-weak contraction mappings and applications, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matematicas, 105, 2, 261-272 (2011) · Zbl 1296.54048 · doi:10.1007/s13398-011-0036-4
[4] Agarwal, R. P.; O’Regan, D.; Sambandham, M., Random and deterministic fixed point theory for generalized contractive maps, Applicable Analysis, 83, 7, 711-725 (2004) · Zbl 1088.47044 · doi:10.1080/00036810410001657206
[5] Beg, I.; Khan, A. R.; Hussain, N., Approximation of \(*\)-nonexpansive random multivalued operators on Banach spaces, Journal of the Australian Mathematical Society, 76, 1, 51-66 (2004) · Zbl 1072.47055 · doi:10.1017/S1446788700008697
[6] Ćirić, L. B.; Ume, J. S.; Ješić, S. N., On random coincidence and fixed points for a pair of multivalued and single-valued mappings, Journal of Inequalities and Applications, 2006 (2006) · Zbl 1129.47312 · doi:10.1155/JIA/2006/81045
[7] Huang, N.-J., A principle of randomization for coincidence points with applications, Applied Mathematics Letters, 12, 2, 107-113 (1999) · Zbl 0945.60057 · doi:10.1016/S0893-9659(98)00157-8
[8] Khan, A. R.; Hussain, N., Random coincidence point theorem in Fréchet spaces with applications, Stochastic Analysis and Applications, 22, 1, 155-167 (2004) · Zbl 1036.60058 · doi:10.1081/SAP-120028028
[9] Agarwal, R. P.; El-Gebeily, M. A.; O’Regan, D., Generalized contractions in partially ordered metric spaces, Applicable Analysis, 87, 1, 109-116 (2008) · Zbl 1140.47042 · doi:10.1080/00036810701556151
[10] Hussain, N.; Alotaibi, A., Coupled coincidences for multi-valued contractions in partially ordered metric spaces, Fixed Point Theory and Applications, 2011, article 82 (2011) · Zbl 1288.54035
[11] Hussain, N.; Latif, A.; Shah, M. H., Coupled and tripled coincidence point results without compatibility, Fixed Point Theory and Applications, 2012, article 77 (2012) · Zbl 1457.54039 · doi:10.1186/1687-1812-2012-77
[12] Lakshmikantham, V.; Vatsala, A. S., General uniqueness and monotone iterative technique for fractional differential equations, Applied Mathematics Letters, 21, 8, 828-834 (2008) · Zbl 1161.34031 · doi:10.1016/j.aml.2007.09.006
[13] Luong, N. V.; Thuan, N. X., Coupled fixed points in partially ordered metric spaces and application, Nonlinear Analysis: Theory, Methods & Applications, 74, 3, 983-992 (2011) · Zbl 1202.54036 · doi:10.1016/j.na.2010.09.055
[14] Nieto, J. J.; Rodríguez-López, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 3, 223-239 (2005) · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5
[15] Ran, A. C. M.; Reurings, M. C. B., A fixed point theorem in partially ordered sets and some applications to matrix equations, Proceedings of the American Mathematical Society, 132, 5, 1435-1443 (2004) · Zbl 1060.47056 · doi:10.1090/S0002-9939-03-07220-4
[16] Lakshmikantham, V.; \'Cirić, L., Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysi: Theory, Methods & Applications, 70, 12, 4341-4349 (2009) · Zbl 1176.54032 · doi:10.1016/j.na.2008.09.020
[17] Karapınar, E.; Van Luong, N.; Thuan, N. X., Coupled coincidence points for mixed monotone operators in partially ordered metric spaces, Arabian Journal of Mathematics, 1, 3, 329-339 (2012) · Zbl 1253.54044 · doi:10.1007/s40065-012-0027-0
[18] \'Cirić, L.; Lakshmikantham, V., Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces, Stochastic Analysis and Applications, 27, 6, 1246-1259 (2009) · Zbl 1176.54030 · doi:10.1080/07362990903259967
[19] Zhu, X.-H.; Xiao, J.-Z., Random periodic point and fixed point results for random monotone mappings in ordered Polish spaces, Fixed Point Theory and Applications, 2010 (2010) · Zbl 1206.54070
[20] Alotaibi, A.; Alsulami, S. M., Coupled coincidence points for monotone operators in partially ordered metric spaces, Fixed Point Theory and Applications, 2011, article 44 (2011) · Zbl 1315.47042
[21] Shatanawi, W.; Mustafa, Z., On coupled random fixed point results in partially ordered metric spaces, Matematichki Vesnik, 64, 2, 139-146 (2012) · Zbl 1289.54160
[22] Hussain, N.; Latif, A.; Shafqat, N., Weak contractive inequalities and compatible mixed monotone random operators in ordered metric spaces, Journal of Inequalities and Applications, 2012, article 257 (2012) · Zbl 1278.54032 · doi:10.1186/1029-242X-2012-257
[23] Wagner, D. H., Survey of measurable selection theorems, SIAM Journal on Control and Optimization, 15, 5, 859-903 (1977) · Zbl 0407.28006 · doi:10.1137/0315056
[24] Rockafellar, R. T., Measurable dependence of convex sets and functions on parameters, Journal of Mathematical Analysis and Applications, 28, 4-25 (1969) · Zbl 0202.33804 · doi:10.1016/0022-247X(69)90104-8
[25] Himmelberg, C. J., Measurable relations, Fundamenta Mathematicae, 87, 53-72 (1975) · Zbl 0296.28003
[26] McShane, E. J.; Warfield,, R. B., On Filippov’s implicit functions lemma, Proceedings of the American Mathematical Society, 18, 41-47 (1967) · Zbl 0145.34403
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