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Some coincidence point results for generalized \((\psi,\varphi)\)-weakly contractions in ordered \(b\)-metric spaces. (English) Zbl 1347.54106
Summary: In this paper we present some coincidence point results for four mappings satisfying generalized \((\psi,\varphi)\)-weakly contractive condition in the framework of ordered \(b\)-metric spaces. Our results extend, generalize, unify, enrich, and complement recently results of H. K. Nashine and B. Samet [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 6, 2201–2209 (2011; Zbl 1208.41014)] and W. Shatanawi and B. Samet [Comput. Math. Appl. 62, No. 8, 3204–3214 (2011; Zbl 1232.54041)]. As an application of our results, periodic points of weakly contractive mappings are obtained. Also, an example is given to support our results.

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
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[1] Abbas, M; Dorić, D, Common fixed point theorem for four mappings satisfying generalized weak contractive condition, Filomat, 24, 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; Nazir, T; Radenović, S, Common fixed point of generalized weakly contractive maps in partially ordered \(G\)-metric spaces, Appl. Math. Comput., 218, 9383-9395, (2012) · Zbl 1245.54034
[4] Abbas, M; Rhoades, BE, Common fixed point results for non-commuting mappings without continuity in generalized metric spaces, Appl. Math. Comput., 215, 262-269, (2009) · Zbl 1185.54037
[5] Agarwal, RP; El-Gebeily, MA; O’Regan, D, Generalized contractions in partially ordered metric spaces, J. Appl. Anal., 87, 109-116, (2008) · Zbl 1140.47042
[6] Shatanawi, W; Postolache, M, Common fixed point theorems for dominating and weak annihilator mappings in ordered metric spaces, Fixed Point Theory Appl., 2013, (2013) · Zbl 1297.54102
[7] Shatanawi, W; Postolache, M, Common fixed point results of mappings for nonlinear contractions of cyclic form in ordered metric spaces, Fixed Point Theory Appl., 2013, (2013) · Zbl 1286.54053
[8] Shatanawi, W; Postolache, M, Coincidence and fixed point results for generalized weak contractions in the sense of berinde on partial metric spaces, Fixed Point Theory Appl., 2013, (2013) · Zbl 1286.54054
[9] Choudhury, BS; Metiya, N; Postolache, M, A generalized weak contraction principle with applications to coupled coincidence point problems, Fixed Point Theory Appl., 2013, (2013) · Zbl 1295.54050
[10] Aydi, H; Karapınar, E; Postolache, M, Tripled coincidence point theorems for weak \(ϕ\)-contractions in partially ordered metric spaces, Fixed Point Theory Appl., 2012, (2012) · Zbl 1398.54065
[11] Aydi, H; Shatanawi, W; Postolache, M; Mustafa, Z; Tahat, N, Theorems for Boyd-Wong type contractions in ordered metric spaces, Abstr. Appl. Anal., 2012, (2012) · Zbl 1253.54036
[12] Shatanawi, W; Pitea, A; Lazovic, R, Contraction conditions using comparison functions on \(b\)-metric spaces, Fixed Point Theory Appl., 2014, (2014) · Zbl 1310.54071
[13] Alber, YI; Guerre-Delabriere, S; Gohberg, I (ed.); Lyubich, Y (ed.), Principle of weakly contractive maps in Hilbert spaces, No. 98, 7-22, (1997), Basel · Zbl 0897.47044
[14] Rhoades, BE, Some theorems on weakly contractive maps, Nonlinear Anal., 47, 2683-2693, (2001) · Zbl 1042.47521
[15] Zhang, Q; Song, Y, Fixed point theory for generalized \(φ\)-weak contractions, Appl. Math. Lett., 22, 75-78, (2009) · Zbl 1163.47304
[16] Dorić, D, Common fixed point for generalized \((ψ,φ)\)-weak contractions, Appl. Math. Lett., 22, 1896-1900, (2009) · Zbl 1203.54040
[17] Moradi, S; Fathi, Z; Analouee, E, Common fixed point of single valued generalized \(φ _{f}\)-weak contractive mappings, Appl. Math. Lett., 24, 771-776, (2011) · Zbl 1296.54076
[18] Razani, A; Parvaneh, V; Abbas, M, A common fixed point for generalized \((ψ,φ )_{f,g}\)-weak contractions, Ukr. Math. J., 63, 1756-1769, (2012) · Zbl 1255.54025
[19] Aghajani, A; Radenović, S; Roshan, JR, 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
[20] Esmaily, J; Vaezpour, SM; Rhoades, BE, Coincidence point theorem for generalized weakly contractions in ordered metric spaces, Appl. Math. Comput., 219, 1536-1548, (2012) · Zbl 06313468
[21] Harjani, J; Sadarangani, K, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72, 1188-1197, (2010) · Zbl 1220.54025
[22] Nashine, HK; Samet, B, Fixed point results for mappings satisfying \((ψ,φ )\)-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., 74, 2201-2209, (2011) · Zbl 1208.41014
[23] Nieto, JJ; Rodríguez-López, R, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 223-239, (2005) · Zbl 1095.47013
[24] Nieto, JJ; Pouso, RL; Rodríguez-López, R, Fixed point theorems in ordered abstract sets, Proc. Am. Math. Soc., 135, 2505-2517, (2007) · Zbl 1126.47045
[25] Shatanawi, W; Samet, B, On \((ψ,ϕ)\)-weakly contractive condition in partially ordered metric spaces, Comput. Math. Appl., 62, 3204-3214, (2011) · Zbl 1232.54041
[26] Nieto, JJ; 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
[27] Radenović, S; Kadelburg, Z, Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl., 60, 1776-1783, (2010) · Zbl 1202.54039
[28] Ran, ACM; Reurings, MCB, 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
[29] Czerwik, S, Nonlinear set-valued contraction mappings in \(b\)-metric spaces, Atti Semin. Mat. Fis. Univ. Modena, 46, 263-276, (1998) · Zbl 0920.47050
[30] Akkouchi, M, Common fixed point theorems for two selfmappings of a \(b\)-metric space under an implicit relation, Hacet. J. Math. Stat., 40, 805-810, (2011) · Zbl 1276.47071
[31] Aydi, H; Bota, M; Karapınar, E; Mitrović, S, A fixed point theorem for set-valued quasi-contractions in \(b\)-metric spaces, Fixed Point Theory Appl., 2012, (2012) · Zbl 06215370
[32] Boriceanu, M, Fixed point theory for multivalued generalized contraction on a set with two \(b\)-metrics, Stud. Univ. Babeş-Bolyai, Math., LIV, 3-14, (2009) · Zbl 1240.54118
[33] Boriceanu, M, Strict fixed point theorems for multivalued operators in \(b\)-metric spaces, Int. J. Mod. Math., 4, 285-301, (2009) · Zbl 1221.54051
[34] Boriceanu, M; Bota, M; Petrusel, A, Multivalued fractals in \(b\)-metric spaces, Cent. Eur. J. Math., 8, 367-377, (2010) · Zbl 1235.54011
[35] Bota, M; Molnar, A; Varga, C, On ekeland’s variational principle in \(b\)-metric spaces, Fixed Point Theory, 12, 21-28, (2011) · Zbl 1278.54022
[36] Hussain, N; Dorić, D; Kadelburg, Z; Radenović, S, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012, (2012) · Zbl 1274.54128
[37] Hussain, N; Shah, MH, KKM mappings in cone \(b\)-metric spaces, Comput. Math. Appl., 62, 1677-1684, (2011) · Zbl 1231.54022
[38] Olatinwo, MO, Some results on multi-valued weakly Jungck mappings in \(b\)-metric space, Cent. Eur. J. Math., 6, 610-621, (2008) · Zbl 1175.47055
[39] Pacurar, M, Sequences of almost contractions and fixed points in \(b\)-metric spaces, An. Univ. Vest. Timiş., Ser. Mat.-Inform., XLVIII, 125-137, (2010) · Zbl 1249.54086
[40] Singh, SL; Prasad, B, Some coincidence theorems and stability of iterative proceders, Comput. Math. Appl., 55, 2512-2520, (2008) · Zbl 1142.65360
[41] Ansari, AH; Chandok, S; Ionescu, C, Fixed point theorems on \(b\)-metric spaces for weak contractions with auxiliary functions, J. Inequal. Appl., 2014, (2014) · Zbl 06780133
[42] Altun, I; Simsek, H, Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., 2010, (2010) · Zbl 1197.54053
[43] Jungck, G, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9, 771-779, (1986) · Zbl 0613.54029
[44] Jungck, G, Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci., 4, 199-215, (1996) · Zbl 0928.54043
[45] Radenović, S; Kadelburg, Z; Jandrlić, D; Jandrlić, A, Some results on weakly contractive maps, Bull. Iran. Math. Soc., 38, 625-645, (2012) · Zbl 1391.54036
[46] Jovanović, M; Kadelburg, Z; Radenović, S, Common fixed point results in metric-type spaces, Fixed Point Theory Appl., 2010, (2010) · Zbl 1207.54058
[47] Aghajani, A; Abbas, M; Roshan, JR, Common fixed point of generalized weak contractive mappings in partially ordered \(b\)-metric spaces, Math. Slovaca, 64, 941-960, (2014) · Zbl 1349.54078
[48] Khamsi, MA; Hussain, N, KKM mappings in metric type spaces, Nonlinear Anal., 73, 3123-3129, (2010) · Zbl 1321.54085
[49] Khamsi, MA, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl., 2010, (2010) · Zbl 1194.54065
[50] Chugh, R; Kadian, T; Rani, A; Rhoades, BE, Property \(P\) in \(G\)-metric spaces, Fixed Point Theory Appl., 2010, (2010) · Zbl 1203.54037
[51] Jeong, GS; Rhoades, BE, Maps for which \(F(T)=F(T^{n})\), Fixed Point Theory Appl., 6, 87-131, (2005)
[52] Khandaqji, M; Al-Sharif, S; Al-Khaleel, M, Property \(P\) and some fixed point results on \((ψ,φ)\)-weakly contractive \(G\)-metric spaces, Int. J. Math. Math. Sci., 2012, (2012) · Zbl 1248.54027
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