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Some fixed point results without monotone property in partially ordered metric-like spaces. (English) Zbl 1293.54029
Summary: The purpose of this paper is to obtain the fixed point results for \(F\)-type contractions which satisfies a weaker condition than the monotonicity of self-mapping of a partially ordered metric-like space. A fixed point result for \(F\)-expansive mappings is also proved. Therefore, several well known results are generalized. Some examples are included which illustrate the results.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
06A99 Ordered sets
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[1] Ran, A. C.M.; Reurings, M. C.B., A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Am. Math. Soc., 132, 1435-1443, (2004) · Zbl 1060.47056
[2] Nieto, J. J.; Rodríguez-Lopez, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 223-239, (2005) · Zbl 1095.47013
[3] Nieto, J. J.; Rodríguez-Lopez, R., Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica, English series, 23, 2205-2212, (2007) · Zbl 1140.47045
[4] Amini-Harandi, A.; Emami, H., A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlin. Anal., 72, 2238-2242, (2010) · Zbl 1197.54054
[5] Caballero, J.; Harjani, J.; Sadarangani, K., Contractive-like mapping principles in ordered metric spaces and application to ordinary differential equations, Fixed Point Theory Appl., 14, (2010), Article ID 916064 · Zbl 1194.54057
[6] O’Regan, D.; Petrusel, A., Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341, 1241-1252, (2008) · Zbl 1142.47033
[7] Harjani, J.; Sadarangani, K., Fixed point theorems for monotone generalized contractions in partially ordered metric spaces and applications to integral equations, J. Convex Anal., 19, 853-864, (2012) · Zbl 1263.54051
[8] Harjani, J.; Sadarangani, K., Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlin. Anal., 72, 1188-1197, (2010) · Zbl 1220.54025
[9] Nieto, J. J.; Rodríguez-Lopez, R., Existence of extremal solutions for quadratic fuzzy equations, Fixed Point Theory Appl., 2005, 321-342, (2005) · Zbl 1102.54004
[10] Nieto, J. J.; Rodríguez-Lopez, R., Fixed point theorems in ordered abstract spaces, Proc. Am. Math. Soc., 135, 2505-2517, (2007) · Zbl 1126.47045
[11] Reurings, M. C.B., Contractive maps on normed linear spaces and their applications to nonlinear matrix equations, Lin. Algebra Appl., 418, 292-311, (2006) · Zbl 1104.15013
[12] Harjani, J.; Sadarangani, K., Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlin. Anal., 71, 3403-3410, (2009) · Zbl 1221.54058
[13] łDorić, D.; Kadelburg, Z.; Radenović, S., Coupled fixed point results for mappings without mixed monotone property, Appl. Math. Lett., 25, 1803-1808, (2012) · Zbl 1295.54097
[14] Ćirić, Lj.; Cakić, N.; Rajović, M.; Ume, J. S., Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl., 131294, (2008), Article ID · Zbl 1158.54019
[15] Malhotra, S. K.; Shukla, S.; Sen, R., A generalization of Banach contraction principle in ordered cone metric spaces, J. Adv. Math. Stud., 5, 2, 59-67, (2012) · Zbl 1273.54065
[16] Malhotra, S. K.; Shukla, S.; Sen, R., Some fixed point theorems for ordered Reich type contractions in cone rectangular metric spaces, Acta Math. Univ. Comenianae, (2012), (in press) · Zbl 1313.54096
[17] Radenović, S.; Kadelburg, Z., Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl., 60, 1776-1783, (2010) · Zbl 1202.54039
[18] łDorić, D.; Kadelburg, Z.; Radenović, S.; Kumam, Poom, A note on fixed point results without monotone property in partially ordered metric space, Rev. R. Acad. Cienc. Exactas Fs. Nat. Serie A. Mat., (2013), (in press), http://dx.doi.org/10.1007/s13398-013-0121-y
[19] Agarwal, R. P.; Sintunavarat, W.; Kumam, P., Coupled coincidence point and common coupled fixed point theorems with lacking the mixed monotone property, Fixed Point Theory Appl., 2013, 22, (2013) · Zbl 1295.54039
[20] S.G. Matthews, Partial metric topology, in: Proceedings of the 8th Summer Conference on General Topology and Application, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197. · Zbl 0911.54025
[21] Amini Harandi, A., Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012, 204, (2012) · Zbl 1398.54064
[22] Wardowski, D., Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012, 94, (2012) · Zbl 1310.54074
[23] Abbas, M.; Jungck, J., Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341, 416-420, (2008) · Zbl 1147.54022
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