# zbMATH — the first resource for mathematics

Some coincidence point results in ordered $$b$$-metric spaces and applications in a system of integral equations. (English) Zbl 1354.45010
Summary: The aim of this paper is to present some coincidence point results for four mappings satisfying generalized $$(\psi,\phi)$$-weakly contractive condition in the framework of ordered $$b$$-metric spaces. An example and an application are also provided to support our results.

##### MSC:
 45N05 Abstract integral equations, integral equations in abstract spaces
Full Text:
##### References:
 [1] Abbas, M.; Dorić, D., Common fixed point theorem for four mappings satisfying generalized weak contractive condition, Filomat, 24, 2, 1-10, (2010) · Zbl 1265.54139 [2] Abbas, M.; Nazir, T.; Radenović, S., Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett., 24, 1520-1526, (2011) · Zbl 1220.54018 [3] Abbas, M.; Parvaneh, V.; Razani, A., Periodic points of $$T$$-ciric generalized contraction mappings in ordered metric spaces, Georgian Math. J., 19, 4, 597-610, (2012) · Zbl 1256.54065 [4] Agarwal, R. P.; El-Gebeily, M. A.; O’Regan, D., Generalized contractions in partially ordered metric spaces, Appl. Anal., 87, 1, 109-116, (2008) · Zbl 1140.47042 [5] A. Aghajani, M. Abbas, J.R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered $$b$$-metric spaces, Math. Slovaca, in press. · Zbl 1349.54078 [6] Aghajani, A.; Radenović, S.; Roshan, J. R., Common fixed point results for four mappings satisfying almost generalized$$(S, T)$$-contractive condition in partially ordered metric spaces, Appl. Math. Comput., 218, 5665-5670, (2012) · Zbl 1245.54035 [7] Akkouchi, M., Common fixed point theorems for two selfmappings of a $$b$$-metric space under an implicit relation, Hacettepe J. Math. Stat., 40, 6, 805-810, (2011) · Zbl 1276.47071 [8] Alber, Ya. I.; Guerre-Delabriere, S., Principle of weakly contractive maps in Hilbert spaces, (Gohberg, I.; Lyubich, Yu., New Results in Operator Theory, Advances and Applications, vol. 98, (1997), Birkh äuser Verlag Basel), 7-22 · Zbl 0897.47044 [9] Altun, I.; Simsek, H., Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., 2010, (2010), Article ID 621492, 17 pages · Zbl 1197.54053 [10] Aydi, H.; Bota, M.; Karapinar, E.; Mitrović, S., A fixed point theorem for set-valued quasi-contractions in $$b$$-metric spaces, Fixed Point Theory Appl., 2012, 88, (2012) · Zbl 06215370 [11] Boriceanu, M., Fixed point theory for multivalued generalized contraction on a set with two $$b$$-metrics, Mathematica, LIV, 3, (2009), Studia Univ., Babes-Bolyai · Zbl 1240.54118 [12] Boriceanu, M., Strict fixed point theorems for multivalued operators in $$b$$-metric spaces, Int. J. Modern Math., 4, 3, 285-301, (2009) · Zbl 1221.54051 [13] Boriceanu, M.; Bota, M.; Petrusel, A., Multivalued fractals in $$b$$-metric spaces, Cent. Eur. J. Math., 8, 2, 367-377, (2010) · Zbl 1235.54011 [14] Bota, M.; Molnar, A.; Varga, C., On ekeland’s variational principle in $$b$$-metric spaces, Fixed Point Theory, 12, 2, 21-28, (2011) · Zbl 1278.54022 [15] Czerwik, S., Nonlinear set-valued contraction mappings in $$b$$-metric spaces, Atti Sem. Mat. Fis. Univ. Modena., 46, 2, 263-276, (1998) · Zbl 0920.47050 [16] Dorić, D., Common fixed point for generalized $$(\psi, \varphi)$$-weak contractions, Appl. Math. Lett., 22, 1896-1900, (2009) · Zbl 1203.54040 [17] Esmaily, J.; Vaezpour, S. M.; Rhoades, B. E., Coincidence point theorem for generalized weakly contractions in ordered metric spaces, Appl. Math. Comput., 219, 1536-1548, (2012) · Zbl 06313468 [18] Harjani, J.; Sadarangani, K., Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72, 3-4, 1188-1197, (2010) · Zbl 1220.54025 [19] N. Hussain, D. Dorić, Z. Kadelburg, S. Radenovi ć, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012. DOI:http://dx.doi.org/10.1186/1687-1812-2012-126. [20] Hussain, N.; Shah, M. H., KKM mappings in cone $$b$$-metric spaces, Comput. Math. Appl, 62, 1677-1684, (2011) · Zbl 1231.54022 [21] Jovanović, M.; Kadelburg, Zoran; Radenović, Stojan, Common fixed point results in metric-type spaces, Fixed Point Theory Appl., (2010), Article ID 978121 · Zbl 1207.54058 [22] Jungck, G., Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci., 4, 199-215, (1996) · Zbl 0928.54043 [23] Khan, M. S.; Swaleh, M.; Sessa, S., Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30, 1-9, (1984) · Zbl 0553.54023 [24] Moradi, S.; Fathi, Z.; Analouee, E., Common fixed point of single valued generalized $$\varphi_f$$-weak contractive mappings, Appl. Math. Lett., 24, 5, 771-776, (2011) · Zbl 1296.54076 [25] Jungck, G., Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9, 4, 771-779, (1986) · Zbl 0613.54029 [26] Khamsi, M. A.; Hussain, N., KKM mappings in metric type spaces, Nonlinear Anal., 73, 9, 3123-3129, (2010) · Zbl 1321.54085 [27] Khamsi, M. A., Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl., (2010), Article ID 315398, 7 pages · Zbl 1194.54065 [28] Nashine, H. K.; Samet, B., Fixed point results for mappings satisfying $$(\psi, \varphi)$$-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., 74, 2201-2209, (2011) · Zbl 1208.41014 [29] Nieto, J. J.; López, R. R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 223-239, (2005) · Zbl 1095.47013 [30] Nieto, J. J.; Pouso, R. L.; Rodríguez-López, R., Fixed point theorems in ordered abstract sets, Proc. Amer. Math. Soc., 135, 2505-2517, (2007) · Zbl 1126.47045 [31] Nieto, J. J.; Rodríguez-López, R., Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23, 2205-2212, (2007) · Zbl 1140.47045 [32] Olatinwo, M. O., Some results on multi-valued weakly Jungck mappings in $$b$$-metric space, Cent. Eur. J. Math, 6, 4, 610-621, (2008) · Zbl 1175.47055 [33] Pacurar, M., Sequences of almost contractions and fixed points in $$b$$-metric spaces, Analele Universitatii de Vest din Timisoara Seria Matematica-Informatica, XLVIII, 3, 125-137, (2010) · Zbl 1249.54086 [34] Radenović, S.; Kadelburg, Z., Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl, 60, 1776-1783, (2010) · Zbl 1202.54039 [35] Ran, A. C.M.; Reurings, M. C.B., A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc., 132, 1435-1443, (2004) · Zbl 1060.47056 [36] Razani, A.; Parvaneh, V.; Abbas, M., A common fixed point for generalized $$(\psi, \varphi)_{f, g}$$-weak contractions, Ukrainian Math. J., 63, 11, (2012) · Zbl 1255.54025 [37] Rhoades, B. E., Some theorems on weakly contractive maps, Nonlinear Anal., 47, 2683-2693, (2001) · Zbl 1042.47521 [38] W; Shatanawi; Samet, B., On $$(\psi, \phi)$$-weakly contractive condition in partially ordered metric spaces, Comput. Math. Appl., 62, 3204-3214, (2011) · Zbl 1232.54041 [39] Singh, S. L.; Prasad, B., Some coincidence theorems and stability of iterative procedures, Comput. Math. Appl., 55, 2512-2520, (2008) · Zbl 1142.65360 [40] Zhang, Q.; Song, Y., Fixed point theory for generalized $$\varphi$$-weak contractions, Appl. Math. Lett., 22, 75-78, (2009) · Zbl 1163.47304
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.